{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 可视化三维样本数据点的PCA过程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from mpl_toolkits import mplot3d\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 在三维空间随机生成100个样本点\n",
    "np.random.seed(8888)\n",
    "X_random = np.random.random(size=(100, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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NF0liNt18rc0s4YtWPicNt89C2m5hc4Wtk/Hm6KXnnnuOD3zgA7z97W8nFArx8MMPF026H/7wh/nVX/1VPvShD+X8/b/+678yPj7O+Pg4zz//PJ/85Cd5/vnny3o/NdLdBqUKGjRNY21tjYmJCRKJBCdOnKh4XrCa7QVN04hGo3g8HkKhEIODgxw+fLjkyvt2r3RLwXaPtsaxtpWVlcxsqnH1ffMQv46jXW6em/KTsqYnWMIJmWNd7pyvLRWvt/ZCIciyXFRPXhRFIpEI58+fp62traR93HvvvUxPT+f9/cMPP8yHPvQhBEHg7Nmz+P1+vF4vnZ2dJe0HaqSbE6UKGjRNY3l5mampKdxuN/v378+EPlaKai2kJRIJAoEAly9fZnBwkCNHjpTVby3Vl/d2J918MC76GFfg9dlUXULr8/mIx+P4fL4MGbtcLu7sdPAzx9t55NVVNA3OH27jbQerk9pRI9382Kme7sLCAr29N1tDPT09LCws1Ei3UuhjX4qiFCVoUFU1k6rb2NjI8ePHsdvtJJPJqlSnUHmlG4lEmJycJBKJYDabOXPmTEWLW3uhp7uT2Dyb6nQ6icfj9PT0ZEah/H4/8/PztCcS/PJwenzK7Zbxb2yUlA6RD29E0rVarUW9Vg8OrTZyncPlfoc10uVm2KAsy1lEW4xUt7W1lZMnT2adFCaTqSqLX1B+pRsOh5mcnCQejzM0NER9fT0//vGPK54meL21FyqFMfYml7mM7oEbDoez0iE256aVEmL5RllIM+63mEp3J8+znp4e5ubmMv8/Pz9PV1d5/h9vaNI1ChrGxsZoamrKepTcDKNUt7OzMyPV3YxqEk2plW4oFGJycpJkMsnQ0BBNTU1ZZuiVotT2wusdhWZmjR64RmzOTZuamkKWZcxm8xbBx2bCuVVzurdqIa3Y9oJ+ze3EZ/PAAw/whS98gQcffJDnn3+e+vr6sloL8AYl3VwztiaTKS+5JZNJZmZmWFlZobu7m3Pnzm178lXzSy+20g2FQkxMTCDLcoZsNx9TNW4E+baznUzzjVDplop8uWn6WFs4HMbr9RKJRFAUJWsuNRqNViRSKBe3qsIulnTj8TgOh6Osfbz//e/nySefZG1tjZ6eHn77t387I3D6xCc+wfnz53nkkUcYHh7G4XDwt3/7t2XtB95gpJuLbPULJldLIB6PMz09jc/n21aqu5MoVOkGg0EmJiZQVZWhoaG8o2nVuhGUI46okW7xyJUorM8Yh8PhTDpEKpXC6/VmZoz16rgaxjK3G3Qfk0Lw+/1lL15/9atf3fb3giDwxS9+saxtb8YbgnSLETQYpbu6fV0wGNxWnbUbyEe6gUCAiYkJAIaGhnZNhfNGWUhTNQ2xwHfuDcS55I1SZ5Po6tq5R37jjHFzczOapmGz2Whra8vMGIfD4Sxjmc1m5JVYLhqP41ag2Ep3L6jR4HVOuqUKGvSRqlgsxr59+0qeYd2MalRBmytLv9/P5OQkgiAwPDy8645KuUhU0zQCgQA2m23LyvxeI92UovLIq6tcmg9gkUTuP9zK8d6tn/GLs36+9KM54ok4mgbTUSv//nTXrhCT/pifb8Z4s+VirhljvTKuJDNtt1DsQtpecBiD1yHplipogPSXNTU1RTwe59ixY5nFp0qgV6iVGq3o0wIbGxtMTk4iSVLJ+WjVhHEhTdM0VlZW8Hg8WK1WZFnOrMzrbmHJZLJqkxzFoFKC/7exdS7O+umut5FSNb5xaZkmp4W+ppsm8oqq8bfPzlNnk3CKEggCT42vc/dQI/uay+sploJCvdVC1pmRSIRgMJjJTNucJux0OrdEu9/KG2exxYvf769VuruJcgQNeqquKIr09PTg9/uzZIWVoFqk6/P5iEQizMzMcODAgS0jSbsNvfJeWVlhcnKSuro6RkdHMz03QRBIpVKEw+Gsf6ampjI6er3SqsYjb7VxfTlMq8uCKApYRQGTCLMbsSzSTcgqKUXFajcRTYIoCIgihOO7c3Mp9wkqn3WmHmAZDofZ2Nhgfn6eRCJtnWlsT9zuqLUXdgmlCho0TcuM6NhstgyR6WbL1UIlogZN0/D5fExOTmas7Y4fP161YysXmqZlHlebm5szYhBIr7rr1ZDZbKaxsZHGxkaSySQNDQ00NTURj8czi0Grq6tZj7w6GeSqskpFJX/bYDezGIhngi9lVduSVGE3i/Q12pnfiGMTVGIpDZPJRHeDrez9loJqj25tN2NsNCKPxWK88MILmScZY2W8E4KEUhEMBmuku5Mwztjqd/5CZLu0tMT09DRut5tjx45ljZdUy+Ogku3pMeuTk5PY7fZM8u8zzzxTteMqp0rSbwITExNomkZnZ2fG8akQ9J6usf+4WVabq8rSxQPGyninPHGNeOehVv7uuTkW/XFUTWOoxcGhjuzKUBAEPnlvP196epYrc1EaHRZ+9b4Bmpy7M8alFxc7DaN1pn4DveOOOzIzxuFwmOXl5S3Wmfr3Vcj7thiUMqYWCATKnp3dTew50tXJdmNjA7/fT29v77ZfiqqqLC4uMjs7S1NTE3feeSc229aKpJoqMiiNdHWjHI/Hg8Ph4OjRozuSgmAkwGKhk63NZuPo0aMEAoG8Ji/b7TMf8j3ybr6wJycnM/OqGdcvhxOb3Y7VXL3TuL3OyifvHWAxEMckCvQ3OzCJWz+vZqeF33zHMBOTIvV1blpbXTm2tjO4FfOyxuo614yxvo6iP8ksLi5umTE2jrUVW6nfDr4L1caeI11FUUilUmiaRjAY3FaqOz8/z/z8PG1tbZw6dWrbgfJqV7rFkLje6vB4PLhcri3V9+bXVmsSopgLdmNjg4mJCcxmc6bihvQj3G6MjOW7sBOJBOFwmMevr/Jvk9OkUjIHmiTeOeyioc5NKpUiFovhcDjK/rzcNhMHbMWRqCjs/ijVrSDdQr4LgiBgsVhoamraYp2pe9/ms87cLryy2BldqJHujkHPuzebzTkjcVKpFHNzcywuLtLV1cWZM2eKulNW+8LZjsSNq/51dXXccccd2yppdLKstI+3efwskVKQVQ2HRcq8f7/fz8TEBJIkcfDgwS19vls5Aqb7qE74kjy/pDLY2YIkCsz740zLbs7ZrSiKkrHW1BeCjC2Kavceb6eMNFXTePTVVZ6b9lNvN/G+E530NlZnAaxcs5t83rdG60xjeCWQ5WMM1Ej3dsHmStIo1e3p6Sko1d1p5CJdowVkfX191kLUdiiXdH2RJC/NBTBJAqf7GzPb0TSN7766wveuraBpGoe76njgYD3zMx4EQWD//v15R9JKVaR5wwpPvrqCKgU42O7i/NE27ObKvpep9RhWk4hZShNPk8PMTEDhPSfamZub49ixY5nEDWOGmu5vYIzt0XuP5Z4rtxPp/tPLS3z9x16cVgnPmsqr3hB/+O6DtLqLc+jaDtV2GCtknRmJRAiFQvj9fiKRCBcuXNgy1rZ5xjgYDJYdFrCb2POka8z2ulVS3Vwwkq6+iDc1NUVjY2PevnKhbZVSpc36ovzKVy8RSypoQGe9jV85KpCSFV6YW+fbl730NNpR5BQ/fHWG0KqZX37rkYLD5aVUur5IkoevBXBYTbTVWXhlMYQG/NydlS12NDrMJBU1Q3jRpMq+5q2fTa4MNWNsTzgcZm5uLutx1zhFYbfbCxLq7US6j11bpdFhxmISwZqOCLq8EOJtB6tDurtxXRlnhtva2lhdXSUcDtPf359ZcA0EAlkzxqlUiieeeIJQKJRR5JXynTz66KN86lOfQlEUPvrRj/Kbv/mbWb+fnZ3ll37pl/D7/SiKwh/8wR9w/vz5st/jniNd/cPUo5xfeumlorK9ikEpPc9C0GN2FhcXmZ6epqmpiRMnTpREtsbjKrXf/IUnPYTjMu4b407zGzG+PSHy/41dZ8qXwB9NEgj6aXdI9LQ0kHI4ilLzlEK6S8EEigYui4QkCnTWW7nqDaEd78j7XcmqRiguY5aEvOm5p/sbuDQfZGo9iiAI1NlMnD9aXFLAdrE9RnPypaUlYrFYhgSMLQrj2sCtIN18+5REAUXN/m7EHIuA5eBWO4xtN2Ps9XppampiY2ODhx56CK/Xyzvf+U7+8A//sOD2FUXhoYce4rHHHqOnp4fTp0/zwAMPcPjw4cxrfvd3f5f3ve99fPKTn+Tq1aucP39+25SJQthzpCvLMpcuXSIej2MymTh79mzVTnq9eq7UwUlVVQKBAMvLy3R1dW3x2y0VkiSVbKe4EkxikQxyXOD5hQQtbgEbSTRFZipoYl9nM/GUSkddce85X3shFxnbzBKaRub18ZSK02rK+32F4jKPXl0hGFdQNY0TvfWc7Nt6I7CaRD7+5j5mfDEUVaO30Y7DUhkhGB93jVEviqJk+o7r6+vMzMyQSqUwm804nU7C4TAulwu3271rpJSvMPjZ4538zTOzRFMqiqLS7LRworc6ysVbZWBeaL+SJNHT08MnP/lJvvrVr/LII49kBDrF4IUXXmB4eJjBwUEAHnzwQR5++OEs0hUEgWAwCKT7xuX66OrYc6RrMpkYGBigvr6+qvOrcDPFt1zS1cfTZmZmcDqdtLe3c+DAAQA8axGenfRhMYnct7+lqD6bpmn888tevvqsH8eL1/jQm/bxtoP5/X6NuGtfA//wYgSzSUsTn6ahySomOU5jvRtFlFkNJ5nxRRlpc/HTdxT3yF9KpTvQbGekxcb4eoKIFkcQ4P2n8p+wz3g2iCZV2ussKKrGxVk/nfVWuuq3Ph2YJZHh1uqP1W2GJEk5/XD1FkUwGGRtbY3FxcVMsvDmFsVOPJbnunG9/WALDXYTF2cD1NlM3H+4lXp7dRYOdyqRoRBkWS7JrlH/XIo91lwxPJsDJz/72c/yjne8g7/4i78gEonw+OOPF308ubDnSFcQBBoaGtA0rWpSWx3lzuqqqsrCwgKzs7O0tbVx+vRpIpEIXq8XgKveIJ/51nWSSrri+9ZlL3/y3mO0121PvP/66jJf+tE0oqKR0FL86WPjuKwSZ/Y1bft3AB+9e4C1cJLHr62gKjJv7TUx5jchmm1YrRZ6zWZMksCHz/XzpqGmjAKrEEohXVEQOH+gnpmNBHVNLXTWWbe92ayEE9Tb08chiQKiIBBOlDfGF07IfOPlJdbCSU73N3DPcOHPrBToFoxOp5Oenh7cbncmWViXPutGM3oVvblFsRNtidP9DZzur/4K/u2ejxaPx8t6mizGG/qrX/0qH/7wh/mN3/gNnn32WT74wQ9y5cqVsm+me450jTCbzSUNTxdCPtKNJhUuzQcAGO2pzzzKqqrK/Pw8c3NztLe3ZyVJxOPxTB/2Ky/MIwjQdoNwVsMJvnt1mQ+d7dv2eJ64vorVdGNEziQSkeGp8fWiSFdOxvnZfpmfbDIzPHyI1pYWvvfCFf7ucoT1SBJVg1841c1bi6ycdZQa1yOJAgONFnq6Cz/mdritzPvjtLrTla6iadTZSr/QYymF//iVK8z742iaxrevLPPxu/t4/6nukrdVCMb+6naqu0gkgnc9yNLiGpI8h5JKZqnudELeDdVdObhVUT2l2DqW4zBWTAzPX//1X/Poo48CcO7cOeLxOGtrayUnDuu4Pb/hIqF74JazOJVve5tJ1xdJ8h//18ushZMAtLgs/OX7jxHxrTA/P09HR0fO2B7j9EI0qWSpmkRBIJYsXMG5rCZkVcMKaKQXmVwFepexWCwTsT40NJSV+jvYZON37m8hZXbhtpnobih9hnMn04DfNNjI966tshRIK97O7muko6707/bZKT9LwUTm5iirGn/9zBwPnqy+9WIxC2mCIPCj2RhPjafFPK3uOj5ythenmcwUxdLSEuFweIvqTh9pu9UTObdqIa3YCrvcGd3Tp08zPj7O1NQU3d3dfO1rX+MrX/lK1mv6+vp44okn+PCHP8y1a9eIx+PbxnoVwp4kXf1CzieQKBe5SPd//GgabyCOy2YCDeZ9ET73v5/j1+7r31Z4YSTdnzzUyl/9YDpNWDcI6M3Dhd3MPnCml0vzQTaiCqKg0eS28TN35u6JxuNxPB4PgUCAoaGhnF7AoijiNAt0dJTvVLaTJuZOq4l3j3YQTiiYJaHsed6ErGLcoyhAQtHQSC8oVoO3+SwAACAASURBVBPFkO7YSoR/G1uns86KKAp41qL85Q9n+MQ9/TRuo7rTwyx10YDuhauPSlZqDFQKbvf2QjAYLKvSNZlMfOELX+Cd73wniqLwkY98hCNHjvCZz3yGU6dO8cADD/Cnf/qnfOxjH+PP/uzPEASBL3/5yxV97nuSdHVU2y8h1/YW/HEkEVLJdFqwKIjgaMqsdhazrXcdaUdR4dFXl7GYRB481c2RrsKP2yNtLv7iF47x7QvjmEwS7z49sqUPnEgk8Hg8+P1+9u3bx6FDh3Y0r2yn04DFGyNgleBEbx0Wk0gslX7CkFWN+0aaCyZBlINi3psvkkQQ0uNbrywGmfXFuOoNseCP86m37GOk7eaCoFHBtdmYXPfCVRSFsbEx4vH4rqju4PYnXb/fX7aB+fnz57fM3X7uc5/L/Pfhw4d5+umny9p2LuxJ0jWuUFa70o3H45n/l2WZfqfMc4kkTqsJq82GllI5UcRChbHSFQSBn76jg5++o6PkY+ptcvDAkWYURcki3GQyicfjwefzFT2nXG6cuxH52gvG97r59TshG07IKq8th4kmFbobbBm5azip8fClZQ62OZn2xbBIAucGG/nkPf1Fb1tWNa56Q/giSTrrbexvc2772Rb63JucFjQNVkMJ5jbimCSBOpsZsyTwN8/O8fvvPljwmPQ5VafTyezsLHfccUf6WLdR3RmJ2Ol0VtSiKIZ0U4rK9aUwCUVloMlBi6ty17Vi5+b3igQY9ijp6tip9kIqlWJ2dpalpSXec6SbEHYev75KKqXw9oNtfOCu3oLbquZjn666gTTZTk1Nsb6+zkCJ+W3VIl0jicqyzPT0NF6vF0EQssQELpcLRVGqTropReU7ryyzHEpglkRenA3wtgMtDLY4+JtXk8RYx2oWkUSBuwYa+LW37Cv6M9I0jW9eWuLKYgiLSSQpq9w70sRb97fkfX0hUtjf5uS+kWa+cclLSlFxWsz0N9kxSwKroWRJAovNr91Odac7fumqO03TsnwNilXdQeGFtJSi8lc/nGF8JYIgCJglgV+5d4DBlsqTNF5PqRGwR0lX/xJMJlPGCLsa0C0WV1ZW6O3t5ezZs0iSxH/dB59+R9o/1l7hEH450NVt4+PjrKysMDAwwMjISMmVSznKtlzb0IM+Z2dnWVxcpLe3lzNnzmTSO4yVl55cGwwGt/gdlFt5LQYSLIcSmfndhKzy7NQGqqaxEVfpbklXWE6LxvPTfsIJJaPMK4TlUJJrS2F6GtK6fkXVeMazwbl9jTl7zMXcUARB4F1HWhlosfNHj3locZqwSAIroST7210l3aCLqfw2B1kaj1VvUZSiutP3u12l+8piiLGVCN316c8tEEvx9Ze8fPrtQ0W/t0oQDAYZHh7elX1Vij1JujqqVenqZjlerxeLxZLTv+FWkC2kXdOWlpZYX19n//79FXlLGCvmcqHLZZ977jm6uroyNyY9AHQ+kCQUF2hxNbG/q4u1tTUCgQA9PT05F4eMRJzrYs8FRdWyFsR0+asoCGjazWpQp8NSlLC6jFYnQlEANLbIa42fRzGkKQgChzvcPHRvP3/3/DzBeJLBZge/fK7wU5MRlcjUBUHI8jXQoavu9O/GqLrTiVhPZslHvJGEnBUiYDdLBOOVn2vFotZe2CVUupCWTCaZnp5mdXWV/v5+Tpw4wfj4+C0fz4H0Y/vMzAxLS0s0NzfT0dFBXXM7f/HkFOPLYboabPzy3f20lzBSVUl7QdM0vF4vHo8HVVU5d+7clgWb715d5ZmpjQz5vWe0nT5H+iLMVXkZq2L9Yk8mk1gsFtxud95+ZEedFYfVxFo4id0sshGTOd1Xz3Crgw6nyFokiUUSSSkab9nfjDOPh0MutLkttLosLAfjuG1m/LEkw61OnHluuqV6L5zub+BkXz1JWS1akGJENbxBosn0dIju0rad6k5vUSSTSV566aUsH1yjKflAswNRSG/bahJZDSe4e6gyQUops8F7JaoH9ijpVrqQlkgkmJ6eZn19nf7+foaHhxFFserJtfqiUykXiSzLzM7O4vV6MxaVoVCI2dlZ/uSxCSZWw9TbzVz1hvjcv7zGH7/3aNG+A+WQru79Ozk5SVNTE6dOneKll17aQriroQTPTG3QWWdDEgWSssp3rqzw8VONeSsWURRzZnPpF7vuAhaJRIDsLLV3HWjksjdCJKlytMvN0a46JFHglw6bmZU6WAolOdDu5P7DpQ2wmyWRXzzdzfdfW2MllOB0fwP3jTRvGwNVav9eFISyCBcqI91IQuYPvjfJS/NBRAF+8VQXv7DN7LLRlNzr9XLq1KksH9zNqru3dph5aj6BD5FT/Y28+472so5TRylq070Svw57lHR16Iq0YpFIJJiamsLn8+Xsi+5UZE8xF4mxR9rd3Z15bIc0OQXiCpOrCVpd6dlMq0tiLZxg1hflYJFzt6WQrp7XNjExgdvtzjik6RH3mxFLqUhC+lEfwGISUVWNlFp6fHeuBILNWWrhcJi6ZJJmsxlHzMXyUgS3241Vgl883V3RQmadzcR7RoubNNltlzHj/jRNYzmUIJpU6WmwpS0dt8F/f3qWl+aDNNhNKBr8/YVF9rU4ODNQ2IPWqLrL5YOrKAoHolFOD4VvEPIGl19azgqxLFV1V2pUz17w0oU9Srr6CaD3EgvB6Lm7b9++vCv+pc6gFoIkSUQTKb7yzDzPTflw20x8/J4B7ui+eUdWFIW5uTkWFhayeqSbtyNq6YF/RQOTcCNyXtNKqpiKJd2NjQ3Gx8ex2WxbUi3yEUyLy4LNLOGPpqizpx/92+utOMwi1VjqzGftZ3wEnp+fJxqNcuHChayq2OVy7ZiQYLdJV690VU3ji09N873ra0iCQJPTzO89cJCObfw8Li0Ecd5ICTHdOORrS+GCpFvMNZEvUdiYm+b1ejNzxjabbUuLIldUT410bzMUOtljsRhTU1MEAoGqee6WAkmS+OunZ/mBx0+D3YwvkuR3/uU1Pv9zR+lusGV8Gzo7O7dVt4miiFXSePdoJ//88iICadewc4NN9DcVL+UtRLrBYJDx8XEEQeDQoUNbLqDt4LBIfPCubr55eYXlUIKBJgfvGW2HZHRH4302V8XhcJgTJ05kjGcCgQALCwuZhGEjETudzooH/qtNutGkwsXZAIqqcUe3e0vCsE66z3o2+O61NepsJkRBYDWc5L/929S2M7/tbivXl8JYTGLmiaWtiFnaSoQRZrOZxsbGLELUjYH0FoUxqsdoDJRKpYpupSQSiaJSWG4H7GnSzQfdfyAYDDI4OJhXpaVpGg9f8vK1FxfQtLQfaU8VCcJkMvHctJ8mhxmTJGIxiayEEvzgyjQD0gYdHR1FZbjpbYr3ne5iuM3JrC9Km9vK2X1NJV3w+Ug3EokwPj5OKpViZGSkrAUJQRDoqLPyK/dmixACydLbC5XCmD7Q3n6zr2isuhYWFohEIlsSI1wu15YYmEKoFukG4zK/8U9XWQ6lvSecFok//tlD9Bg8MnTSXQikI+J1lZ3DLDG1Ht12+w/dO8B/+eY1QnEZVdM42unmJ4swPNqJqB7dGCiX6k6/Wfp8PhKJBMFgcEuLwrimcKsy+8rFniTdzSd5JrYlGsXj8RAOhxkcHMzpP2DEk2Nr/OUPpnBYTAjA3zw7w/3dCm+qUvUiSRJ2s0BS0ZAkSMTjRCJRRNXBXee2muTkgz5fKwgCAvCNl7yE4inePNzMf7pvEGsJtoxG0o3FYkxOThKJRBgeHs6aLKgWCinSkrLKUxPrzPpidDfYeMv+FqwFepOboWkakRur5tshX9VlTIzwer0Zee3mqrjaDmCapvGdKyt8/SUvqgatLjML/hjNrnSLIBBL8dfPzPFfz+/P/I1Out31NsQbXh6iIBBNKhzt2v7JpK/Jzl+9/xjXl8NYTRJHOl2ZCYbtsFsS4M0tJLvdjqqqdHR0ZKri5eVlIpEIsixjtVpZX19nbGwMQRBIJpMl2zsWiuoB+Md//Ec++9nPIggCo6OjWwxxSsWeJF24eTGbTCaCwSCzs7NEIpEtzlrb4Qfj60iimLlYk4rIK2upqnn0SpLE+4+38MWnvSz7EkiSiSO9LfzM3Ucwl9iL1TSNqbUI//mfrqBpYJIEHr7k5dpSiK56O06LxHtGOzjYmd/TQd+O0a9haGiI1tbWHWu7bEe6mqbxP5+f55XFEE6LxCsLIabWYvzHe/qK9kkIxFJ88akZpn1RJFHgZJ3MqRyvSykq3kACm1mk1WXJuTBknF2VZTkzQWF0ADOalLtcroqqrB9O+vgfT8/isKZv+i9MB7CYbr5viySyHklP58RTCt+9usqY10eHTeMX7mng/sOtfPfaKqIg0Oq28Gtv2Vdwn/V2c1ELZ0bcish3ICNn3k51d/36dRYXF1lbW+Oee+5BlmU+/elP8+CDDxbcfjFRPePj4/z+7/8+Tz/9NI2NjaysrFT8vvYs6UK6fxeNRrl69SojIyM0N+cf7cmFerspa+hdUTXcVqkqHr26+sceCvB/3NVM0FRPvdPKm4eaSx4X0t/TizN+UoqK25aukKMJhR/PBDhw2kVCVvmbZ2b5tbcN09WQe3ZXVVWCwSAXL17ctR73dqTri6Z41Ruiqz69yFVvNzG2GmEllNx2QciILz83z8xGlHa3hZSi8fiswlvXowy23DSRWQ0l+H++M8ZqKIGqwTsOtfCJe/q3JXaTyURDDgcwo0n58vIy0WiUF198cUtVXMxTzDOeDSTp5k3fbZPYiMrIioogCMRSCnf116OoGp///hTXlsKIqsyFpEzUNMdD9/bz83d2Ekul/SeKqVrLwa00u8mXGqGr7kZHR+nq6uLy5cs88cQTGQe2YlBMVM+XvvQlHnrooczTUbkeukbsWdK9fv06gUAAl8vFyMhIWTN6v3Cqhx9N+vBF0l65TquJ8yO2isbG9Jh1j8eTiRbq7y/ebGU72G+sPOuIpRSs5nQUuVkS8cdkZtYjW0hXn/1dWFhAFEXOnj27a5VLQcObHLxXym1gbCVCizNduVpMAhoaC/54Fun+xVPTLAcTNDjMqJrGo1dXOd5Tx5sGSxvez2VSfuHCBY4fP571+GusijdLn43fX73NhKzcbPekH/lt+KIpFFXjXUfa+IWTXcxuxBhbDtPhthCPqzjNJp7xbPDgya6C6SPVwO2aj6bDqEbTF0uLQTFRPWNjYwDcfffdKIrCZz/7We6///5i30JO7FnSHRwcxGw2c/369bJJsrPexl/94ihPT/rQbkwDrM1NlrU9XUTg8XhoaGjgxIkTrK2tVex1YMR9+1v4++fnWLiRiABwpPPmCaZqGjaDUEJVVebm5pibm8s8Pl2+fPm2UNwBNDnMHO10c3khhMMiEU0qHOpw0eou3p2q1WXBF03SYE8TqqYJNGzKBZtaj+G03ph5vqGWm9sorhoqBvkef42+uKurq0Sj0Syfg7ftc/CjSYn1SBKB9MLZZ//dfnoabGg3jjW9rex1DOHGP3mUyVXH7W7rWK4wopioHlmWGR8f58knn2R+fp577rmHK1euVKR+27Oka7PZMmF5lVSmLS4r7x69GcroN5lKIkpN01hdXWVycpL6+nruvPPOTJKFblRTLbisJv7HB+7kkStLBOIyXfU2fjC+zrw/hqbBYIuDI511WQGZHR0dnD17FtON91Wpy1ip2K7SFQSBD53p4alxH7MbMbrrrbxlf0tJvrf/4Vwvf/Z9Dys33LqOtYhZNyKAgSY7rywGaXBYUDUNQYCePC2YYhCIpRhbidDszH9zyOeLa/Q5IOznYwc1XllNk8vJXifmRIBIREk/Vt/4HHobbfQ02JjdiCEoCjFZ4+xQHQ323bl8b3fSLddhrJionp6eHs6ePYvZbM7M+I+Pj3P69OmS96djz5KuDj2yp5rbK4bEdUeyyclJ3G43x48f3zInaPTUrQY0TcNlM/G+Uz2Zn53qb2TWF8VqEjnQ7sK3lq62W1paOH36dJaBTDWsHUtFofaCWRL5yYO5bROLQX+Tnc/91AEW/HHsZpGVyStbqpX/dN8A//e3X8MXST+2v/1gK+cGyxukf3k+wCe+egVBgJSi8aZOgVKuv80+B/uBnzBYMeYzBPr46SYe90QZX/Qx1GLnA28e2NXUiNs9H60cYUQxUT3vec97MsGUa2trjI2NFQwwKIQ9T7pms7mq1WQhlZsuj52cnMTpdG5RbG3eVrVIVyevzRdae52VNreFtbU1fvziC9TX13Py5MmcozPVvEg3H0u10ipiKYWnxteZ30gHVL5lf0vBJIk6m4m6jnR1u+rZehxtbitffN9RFgJpYm53l69O+/WvXyViyLd7ZhGem9rg7L7y1VD5rBiNhkDhkJ/j9jAjHREslhRz056qGZQXgqqqtyQws9gKOxgMbjHrKQbFRPW8853v5Hvf+x6HDx9GkiT++I//uOLRyj1LukZPXd0QpRrYrtLVvQjsdjtHjx7F6XTmfJ2OapJuPh8Hn8/H+Pg4DoeD0dHRvDeAaiIXYemVmsvlyjrGUkhX0zS+dXmZGV+MJoeZidUoa+FFPnSmp+KVeYtJRAR+MO5DVjXu6K7jSGdpXraKqmVGuHSoGsz4YhWRbj7kMgTyeDzY7XasVuu2hkDVjHnXwzJ3G6WkRvT1bZ+snQ+FonoEQeDzn/88n//858vafi7sWdLVsRPpEYlEIutnPp+PyclJLBYLR44cKXp1tJoGOptbA4FAgPHxcUwmU0nHVA3oIgv9qUC3oLTb7RlTeafTmTagsVqLbmlEkgozvihd9ek2jc0s4Q3GWY+kih4hy4elYJyHLy/jtpmQRIHHrq8iCHCks3ipsyQKdNRb8QZunh8CZGWc7TRUVcVqtRY0BJqbmyOZTGY8cY0TFKX2Z29VT7dY+P3+THzRXsCeJV1jpbtT4ZQbGxtMTExgNps5dOhQycS2E5VuOBxmfHwcVVXZv39/WY9VlUIQBBRFYWFhITMZcebMmXRw5w31XDQaJRQKsb6+TigU4oUXXtgiLNgcFZN2KEsbkkuicMPUh6z4+lyY98f40o/m8AYTNGgp9h+Vqd80weBZi2KShEyChKqZub4ULol0Ab7wvqN89H9dJiGrpBSV8wMSJ3p3z1JQVdW8Zk3FGALp0udSDIFuVU+32Cp9L3npwh4mXR07UelGIhEuXryIKIocPHiwJOMXI6pJuqqqZsbjRkZGSlo40DSNy/MBZnwxVtZlTitq2Y/rmqaRSqW4cOECbW1tGe8IYzVrdJxqbW0lHo9z/PjxLcKCWCyWJbd1u92c7a/j6akAZkkkpSiMdtfT7MwvNAjFZT73yDixlIrDLHHNp/D5Jzx89t/tz7poLSYxSwiTUjRs5tI/g/1tTh77T2eY34jR6DAzefVSyduoBMVkshmRzyZTlz4XYwh0KyrdUhZ891JqBLxOSLdalW4wGGRsbIxIJMLJkycrriIrIV1F1Xhp1s/cehg1vEa97GdkeJi+vr5MnzSSULCYxII+qv/yyjLfu7aCRRLxLitoz8zyy3f3I5aSY0O6pz0+Po4sy5w8ebKom5FxAXCzsACy5bYLCws4IhEOmWXigoX2FjdHO8RtNfUzvhiRpEKTIz2lUW9JCyY256IdandxZTEdey4KYBJFTvXlvlBTisrkapRoSqGzzkpnffZ4mdUkMtSabilM5nnfiqoRisu4bKaClXopqIYkt5AhkP5d6FVxKpVCkiQSiURZhkDloFQD871i6wh7mHQzGVZVCFsMhUJMTEygqioDAwPMz89X5bG93BEtTdP4yvMzPHl1ASWVxGp3crDRzQm3G0EQ8EWS/F8PX2V8OYwoCnzinn2890RXzm3Fkgrff22Vrvp0okMqCFe9IRb8MXqbilt0029GJpOJY8eOcf369aLNevItpL0wvcHjr63jsEi893gHvT03CfDEjUosFAoR8PtZmJ/PxPhs7k9aDTaFgiCg3hASbL4ROa0m3neiC89aBFmFvkbbFttESMev//PLS0yuRZBueFU8cEc7h3IYxedbILy+FOazj4wRisvYzRK/dX6E0e7qtIGKJd1YSuHbryyzGEhwrMvNW/cXlsjnMwR6+eWXcTgcu2oIVIoUPxgM1kh3N1HJHTcUCjE5mVagDQ8P09DQkIkUv1XHJssyL12b5LGXFxhob6DO3YamwdX5VXyRJE1N8HuPjjG+HKbOlvaO+MsfTDHS7swyR9ehaNoNddPNYxKENLkUQjQazbJ81FU/+W4mud5vLtJ9anydP3rcg0h69f+HEz7+288fzlgYGisxI4wKL32WVQMGHHDNF05XY0n46Js6czqOOSwSR7u2J7/5jRie9Si9jekbUjyl8Ni1tbyku/k9x1MKv/Wd10jKGnU2M7GUwm//yxh/+8HRLX3mclAM6aYUlU//83XGVsKIgsB3r67iWYvysbtLX+HX3197e3vWjbZYQ6BiI943Q5blolsa0Wh0z3jpwh4m3UrINhwOMzk5STKZZHh4OOsuWWwaRbVhjOuxN3XQ0tJKnctG2swxraJKyemK/tXFIC6rKZ0AIAmoCYXxlUhO0nVaJA53uHnVG6TBbsaf0BhuN2fiy3MhkUgwOTmZibU2Kqqg9NnbzfiHi4tYRCGT7eaLpnjitXV+6UzPtn+Xa5ZVURRGRsL8cHwF70YEayJKZ3yWy5dXcLvdJXvkphQNyfAyi0nEH0vlJNhcP1sJJUnIKk5L+tKymyUiSRlvILFrpPuqN4RnLUK9zZSJkf/Gy0t86ExPybaZkHshrVhDIL1vb/SgKMYQqNj2gn4e3i7S9mKwZ0kXsvuFxZyMkUiEyclJ4vE4Q0NDOYecdzNZAtIX0cLCArOzs5m4Hg2BvkUPcxsx6m1mAvEU3XUW3Jb0sbW5rSwF4jitphsLK9CSR5IqCAIfPNvLv15ZZmI1wnCjiU+8uS+nB69e5a+srLBv37685u/5SDcXCeV6raJlFK6Gz6E8EpckicaGeh44nb7hXLhwgVOnThGPxwmFQlmPxMUkR3TUWbGYJDaiKRwWidVwguPddXlN8Df/vMFhRtPS1aZZEpFVFVWDpm0WA0tBcZWuhjEOXX/KyRcjXwjFLt5t17cv1RCoVKe/3b5uK8GeJl0d+piXUfJqRDQaZXJykmg0miHbWxUmaPyZ1+tlenqa1tZW7ror29T8A2d6+YNHx/jxnJ+uehs/d7QOtPQj/f95/37+89evEE0qKGraqOee4fwqGZtZ4mfuTPd8X3wxgNuaTTS6Mc78/Dy9vb0FXcjykW4+gt6M94y284Unp1FVDUVLL0zdt796BurGi99oxZdroUjTtMz4lF4ZP3iyiyfG1gjeiHa/dyT3seX6XutsJh76iX6++NQMSSVNuB8510ubuzrigmJI91CHC7dVIhCTsZhE4imFU/0NRadG50Il10s+QyBjZM9mQyB9DjyVSm1bFZfShrhd8LogXX1sbDPp6skI4XCYoaEhWlpadv2OqPc/9RPD6EbW2NjIqVOnthy3pml87cICq+Ek/U0OIkmZv7/k51N3p193sMPN3334JK8th3BZTRztqit6EsHYj9U0jaWlJTweD+3t7UVFB23eho5SPtf7D7VikUS+d20Vu1ni/ae62Ne880q6XAtFRlHB+vo6MzMzpFIpDlssuLvcuFwqyXgM0yZbRsifj3b/4TaOddWx4I/TUWelr4Qcu0IoJpPNZTXx+fce5i9/OMNiIMFot5uPltHP3Unki+zRDYHm5uaIxWK88sormZQIY2SPHmRZrgT4VmJPk64xPcLYh43H43g8HgKBQElJEsbtVsst3zjnqI9cuVyuLDeyzYgmlUyFKwgCTquJ2dUAcxtx9OCWZpeFN7lKrw51wlxbW2N8fJyGhoYtxjiFUGlPVxAE3naghbcdKN/oplowigo6OtKx63oqQSgU2lKFGdsTZrM573nV3WCjuwIns3wo9lG/s97G537qQNX3v9PQDYH0Pnx7e3vm+9AjlfRF1Mcee4yLFy8SCoV4/PHHGR0dzWprFEIxUT0AX//61/n5n//5TOuqUuxp0tWhV7p61Lrf7982kLIQCrUrSt2Wz+djbm4Oi8XCsWPHCno26HOdqgaScHOxQKByA1VZlnnllVcq8mqolHRvdxgNaDZXYcZFomAwSDQa5ZVXXslqT+xE3PvUepTrS2EWVhVGZTXvbPZiII43kKDOZmK4dWt1ngvhhIxnLYooCAy1OrAb+v236ns29nTzGQIdPXqUb37zm3zlK1/h0Ucf5Y/+6I/4zGc+w5vf/OaC2y8mqgfSE05//ud/zpkzZ6r23vY06RpzrmZmZkgkEgwODlYcQ1Mu6W5+9AuFQgQCAVKpVEmR5lazxPmj7Xz78hIWSSSlqAy3OOh0ll9564m/4XCY/fv3b/ENLRaroQQXFhO4Qj7uGrEWPev7eoAkSVm9yVgsxvj4OENDQ4TDYYLBYJa6yzg9UYkT2IXpDf7wMQ+yqhGPpRhLvMbv/vSBLcR7YcbP3z03D0L6hv2WkSZ+7s7Oba8FXyTJF38wQyCWQgPaXBZ+5d6BjLCk2hHzxaKYhTS73U5nZyejo6P8yZ/8SUnbLyaqB+C3fuu3+PSnP13y9rfDnibdZDLJxMQEXq+XlpYWTpw4UZUTpFQl2cx6lD//Nw+L/hgDzQ4+eraT8EracKSuro7BwcGSpcTvvbOL3kY7k6sRWl1WjjYL+H1rJW0jpah86+V5nr42j01I8Uv3HMBisZQ90+iLJPnGy4v4QjJuLcHDl5f46WPt9DfvnuHL7QT9UT9XsKW+aBcKhbKcwIyr9boTWCH81Y9msZhEGiwSASXGxGqE56f93DN8U9qbUlT+/oUFGh1mrCYRVdN4ctzH2X2N9Dbm/76feG2N0A1DfEhXyj/y+HjX4fR7ud0NzMuVABcT1fPSSy8xNzfHT/3UT9VIV8f6+npG459IpKmQkQAAIABJREFUJKp2Ry7FRCeaVPj9R8eIpRSaHRJjC2t85purfP69R2lva+H69etlKeYEQeDMvibO7EtfWH6/H18J6jZZlvnzf73EjzwB2hpdhEU7/+8Lq/ziSPlG5hMrYdCg0S7hsEloJonLC8E3NOnmO+f0RTvN4mQ6GUKwwJEOF2YtmVm0m56ezlok0ivjzYKCcELJTB4IQrrJFElmn58JWUVWtcwcrigISEL6/NwOG1EZu8GDwmoSCcZubnsv5aOVgkLTN6qq8uu//ut8+ctfLnnbhbCnSberqwtZllldXU3Hn1QJpZCuNxAnFE9i1VIEYkna6l2EUgKaNe32VC3Tm2K3o6oqs7OzzM3P8/KSxIHeNkw3zG2WggnmQxL9FaRHaGgIgggaWTle5SKSkPnxXBB/LEW728rxnrqCXhK3Cwo9ei8FE3z++x4icQVNSAdR/sbbBuk0OJttzlLLZQQ02mnn+dkwjU4LcVnDYhK2KOScFomeBhveYIJWp5lwQsEkiQUtMQ93uri2FMJpkVC1NEkfaL95E73dK12/3093d3fJ2y8U1RMKhbhy5Qr33XcfAEtLSzzwwAN861vfqngxbW+c3QWwE05jxZBuKpViZXGWQDCMKJlobm5GNFnQNDKVSbWsJwv5OGiaxuLiIs8++yyKonDu7FkcDnvW0pumaZgksezFkf3tbiRRxBeTWY8kiSQUjldga5hSVL4/ts5yKIFZFPCsRXjG43vdLNI9fn2NpKzS1WCju95GJCHzb2PrWa/Rs9RaWloYGBjg2LFj3HXXXYyOjtLR0YGmaZzvgwPuFOv+IFZR4z+MOnGqERKJxM1FVkHg42/uo6/RxlIwgcUk8qs/MVBQBfemwUbecbgVX0wmGJd59x0dWT4Rt8rWsZTUiHIqXWNUTzKZ5Gtf+xoPPPBA5vf19fWsra0xPT3N9PQ0Z8+erQrhwh6vdHfDUzcXFEVhZmYGr9dLX18f//7uYb51eZloKG1u/f7TPdTdONl3utLVs9omJiZobGzMGv96z2gn/3hxHotJJKVo9DbaGWo2ld1eaHCYee+dXXz/x2FMFgtnD3bRUW/LxM4vLi5mepa6gfl2lWAwLhNJKLTdSP9tc1vxBhMkZBVbDsVcIWxEUzzrlZl8cZGDHS5Gu907ughUqNKNJOUsC02zJBZ83NdhFBT09MDxo+mnmAsXLjDQ35hlyWg0Kv/E2XZsdjumIqtTURB41+E27j+UHrXa/H6MM+a7jWK+u2AwWFYScDFRPTuFPU26OnYjPQKylVvd3d2cPXsWSZJ4sEfjzr5GVkIJuuptDLfdNJLWVTWVIlel6/f7GRsbw2az5QzGvP9IG21uC1e9YZqdZn5ifwsri3MVhVM2OS2c6k0vAHXU29jY2GBsbAyn00lfX19Gfru4uJghhHg8ztLSEm63O0vqaRKFG7HpafKSVS3diyzDCjEUl/nvP5plak0laI7w8nyAWLKdc4NNhf+4TIQTMheXksxqKxzudG9ZsDrRW8+l+SBWSUQDYrLKaE953sxAZia9vb09y5LRGGo5MzOTFWppnKDYTtm1nYH57az4qsRLt1BUjxFPPvlkWfvIhT1NuvqJUk1PXdiau6Y/uk9PT9PR0bFFuSUIAgc73BzM4UQlSRLxeLzkY1BUjR+Or3F1KUSjw8zbD7ZkKl1jesR2o2iCIHCyv5GT/TcVWNVIBBYEgVgsxksvvYSqqhw5cgSn05mZ1jCu4ieTSS5evEgikWBtbS0jMnC73TidTjqdAvOBOGZJRNHgZG9dWQbrk2tRAvEUTXZodJixm0WemvDtGOmGEzK//8Qs8+sRbNMLWCSB33zHMAc7bt5wT/XVE0spPPHaOgLwwdPdFVk85hPs5DMqj0QihEIhVldXmZqaQpblvC5gsZTCo6+uMrcRo7/ZzrsOt6WN328B6ZbSXtprXrqwx0lXR7WjxXWnMf2x2ePx0NzcXLJyy7itUvHty16eHFujwWFmej3KxEqEs84UV65cIRKJMDIyknWRFYtKP6tkMplZ7Dl69GhmWD3fhWKxWDCZTPT392d+phughEIh2giQSIaJpVRa6hw4kgo+Xwq32120Z28auoDkZsW2k63hpyd9LAWTNDsk3G4rwbjM/7qwwO/89E0VmCAI3DvczL3b+GKUglJUkrlCLfO5gAmiyDc8MBtUcdrM/HguwNRajE+9ZeCWpUYU+z5rpPs6gSRJRCIRnnvuOerr6zlx4kReyW4hmEymknu6qqrx9KSP7gY7kijgNIuML6zT1RDjjkP7S5Y1GyGKYlntDmMfu76+nvb29rKjqLP6lcARbnog6DLP6elpUqkU8zEzIc1Cf4ubs8NteS0ah1qc1NvMTK9r2KMpQgmZd9/RvuV11UIkqaSd0m4ci0USCCcqf9p6bTnMd6+uEpdVjvfU8Zb9zZnKv1Jpej4XsNn1MItXXqPFISErSZBTPH09xMm6EPUWsNlsJBKJqqULF0IpqRF6AvVewp4m3Z04AXw+H6+99hrJZJLTp09XHGlezkKaIKRDGmVFIRRMVyWSyY7Dbs/q5ZWDUitd3Q1tamoqYz25tLSUk7grWXTJFaz4t8/M8r9f9aKqCTQ1yL1jS7y9V8BsNmd6lXqf2G0z8fE39/E/H1uhrcXBoU43o93ZbRdN01gOJYkmFdrdFpzW8k//Y111/G8gnlKxyiobsRQ/O9pZ9vYAFvxx/uGil3qHiTqbxNOTPiRRyHhUVMsPRIemaUSSCggSZrMZh9OckXgroSR9fX2EVxeIxWJcu3Ytky5s7BPrxjPVRLHOYXvRSxf2OOnCTR8APban3Is+EAgwMTGBKIocOHAAj8dTMeFC+dMLJ9tEHr60SIPbgdnRxHCjnS7bSsXHs5l0IwkZjbQz1WboBj319fVZrZXN3guapqGqaia00rgv/cZYqpx0LZzkny4t47aZkcS0EfezKwofe8cdNFiFjBnN2tpa+hFZEHC5XJxqUTl2IN0vNu5P0zT+5coKT02sIyBgM4t87O6+bdVa22GkzcnHzrTxDz9eRtU03n2snZ853lHWtnTMbcRA0HDeGDdsdVv4/9n78vA2ynP7M9o3W973fZGXJE6c2FnYKSVhaQPtLYTyK5RSKOWSQguEQBcaWra2lN5bQoG2aWkvFwJtKeRCCJRCwhY7wQmQxLHlfV8lW/s2y+8P5RtGsiyNbHmJo/M8fsCxLI3GozPf977nPefkkJ0n3ViO5I7ZPHjq/R4MWf1yvSSVDMNWL9QKCVxeFjW5CShI16PbMQGdTsevjIVGQMR4hqKogEm7hISEWUX3LGUvXWAJkC4BaaZFS7rCplRZWRn0ej0YholZYy4a0uU4DmNjY2hvb8eK1BQUX1qDLrMHyRo5zipNxQcfjWK/cRwSClhdkBSSKCOBkC7NsHjyQCfeah4DBeDs0hTcdXE5FDIJ7HY7WltbIZVKUVNTM+XmQ56DkC0hcblcHkDAHMfBYrHA6/XyZCyVSgPy7aaD1U1DQoFXMkglFKQUBbuHQUaCBqmpqQHlDZqmcbR7DE8fH4Xn2HEUJgBfKpYhTe/v4Jt8crzTakJOkhoSCQWLy4f/PTyAezeWRX0OCWqytSg6N42f358t1AophJsQl48NMKeP5Ur3mQ96MWb3IStRCbePwaSLxvnlKZh0+VCcqsEl1Rn+1ImghYxCoZhy7okdI3FkC27akZWx2PQOsaQ7XRz9YsdpT7pCe0efzzdtamwwiLG5y+VCWVlZQFMqlo05sTXdiYkJtLW1QaPRBNSQ64r9Px+yuPFfRzzAMSM4AOkJSvz26hokaaJLJCDv7bVjw3ireRTJWgUoAO93mJCVqEC93gGHw4GKioqwUhyWZcEwDL/6El78UqkULpcL7e3t8Pl8WLVqFeRyeQBRA+DPC/l9iqJ4UsnRK5GoksHioqFVSuE4le6bow/99zW7GPzu4Ci8LIWsVD0GnF58ZNPhezXZsNlsGBgww2q1QuqxQCaVQS6XY9AqgdPlgnqG6baxNoOpytShKUWFPrMbFOXX9W6s+rz2GivS9dIs+ifdyEr0E7pKLoXExaA2Xz9FXSFm90jsGIW+tsKmXbTpHWIXTzabLWpPk8WA0550CcTKxkj+l8Vi4fO/QkXMxAqR1At2ux1GoxEAUF1dPW1T4M8f9cBJc8hOlAMUMGL14G9NA7j53KKojoeQ7vFBG+RSCSQk8oih8d6xblx6ZdW0jTpSUlCpVGhvb4fJZEJiYiISEhKQmJgIjUYDlmXR1dUFs9nMG8eHgpCAQxGxjKLw4JfK8Yu3u9BndiM/RYX7NpZBJZfC4vLhQJsZ4w4vCpNVOKcsFZ3jTtAsC7XMr/PN0CpwfNAOlca/7V2jScaB4U6kaBSQgsXQpAMZag5tRmPAgAHp+GtCmJaHOh+RHuOlWfzmnU68126GXi3DXReVYk1BaDG/QibBdWvz0DHmhI9hkZesRrLgphor0pVLKSSoZHB4GeiU/nBThuOgV02lg5lOpE3XtIuU3qHT6XiXtkiYnJycsUZ3IXHak65wKi1cV97r9aKrqwsmk2lWXrszPb5gkJWgy+VCeXl5RNnLmM0LmYTyex+AgkwCjNmnDnBEAiHdvCQdPuo0w+1yw+PxwMfJsKo8nzfyDoawlKDT6bB+/XrQNA2bzQar1cqbxhOtbk5ODuRy+bQrJfJBFv4suGSRq1fit/9Ryf+coii4PD7sbhr0r3yVMnzca4HVzaAsXQOWAySnbgz+qTYJHzKZrVdhy5oc/OPoEBgWyE/T41sb8nlSE9Yqg+vEhIiDV2ViSPfRt9rx5skxABTMTh9+8I9mPHvdSpSk+Us2Dg8N46gDXppFfrIKOUlqlKZrcLhnEu+3m1CUqsGKnISYGutTFIWbzsrH797rwajXC5bjsKkqDYUhEi5iPZEWKb1jYmIC4+PjYBgGJpMpoDwRfCOczWDEQuK0J12C6abSaJpGT08PhoeHUVRUhPLyctEX7lx4iQrJv6ysDOnp6aJeY21xMo50j4FhOIDiwLAIGHoQC9JwvLBQgbeOujHmpMBQcmgUMpSka+Hw0AFd/eC6rbCUIJfLkZKSApZlMTIyguzsbOTn58PlcsFms6G/v583ItJqtfyqeLpGSyQi5jgOozYXJhxeZCX6yyKZOjmMozZcVJGCVbkJ+KDVDtrugQQU/vP8woBzW1eQhJW5iXD5WOiU0gCznlC1SqGeOHhVlpCQAK/XG5GQ3jGa/GUTioIUFHwMi4auCZSkaeD0Mnj9xChcXhZyKXB8yIYLy1Px+okxHBu0QSbxD8lcUZOJy5ZnxrSmW5GpwwOXGzBk9SBBJUWuPnSJZT50usHKFZIerNfr+fLE2NhYwI2ws7MTPT09M2p2R0qMePzxx/HHP/4RMpkM6enp+NOf/hSgM58tlgzpBvslMAyDvr4+DAwMIC8vDxs2bIjqgg3ONpsthDrXoqIiGAyGqAj9qtU5ONbWjSPjNKQSCa6pzwuo94mFw+GAyeQngp3fqMfzR0dhc/lQlqGD2eHD2y1j+NKKLEgoTEu2BDabDW1tbVAoFKipqeHHkJVKZcAKxOOjMWm1w+vyC/Lb29vBMAxPXoSMQw2eBBOxRs2Ckkj833McfAxAAZCCwy3rs5DuG0FuUTZK0rQoTtNOISq5VCJ64i1UoKJQT2w2m+FyuTA2NhbQNBL6TihlEvg8pw4Sfq8DkswwMOmC3cPwdWqnl8G/jeNoHrIhR+/XxNIMi9eOj+GLlekxl4wlaeQRewKEdDmOw2eDNgxZ3MhMUGJlXuKsHeamA2mkhUqLIE27Tz/9FO+88w5OnjyJ2tpalJSU4KmnngqYhpzu/URKjKitrcXHH38MjUaDp556Cvfccw9efPHFmL2/0550hasuh8MREGmenZ0tOmwxGITEZ0u6LMvC6/WioaGB17nO5DllUgm2LEvAvSUl0Gl1ooMoCUjKgdPphE6nQ01NDSwuf8x4SZrfyk+rlGHY4oLF6Y97CdUkAz6vizudTpSXl4c1HOk1O9HYNQmW45CgkuPcsjIknHpup9MJq9XKD0N4vV6oVKqAFXFwxzsjQYmqrAQ0D9mgkEngpVlcUJ4G09gIhoeHcVldOVJTU/1aU0GjDwjdsIsWwlUZWYHn5uYGRL4LfSe+VqHCnz+1we3zKzAydAp8sZJIwADhmaUogGb9xEyOWXqqpESzXMxJVwxITfcfnwzj7Ra/coblgPPKUvD1upw5KdGFG44gTbstW7aApml88YtfxJ133skHvUaCmMSICy+8kP//9evX47nnnpvlOwrEaU+6BFKpFJOTk2hoaAgZaR4tCOmKVUMEg6T+dnR0gOM41NXVzfi5CCQSCcBxURGuz+dDZ2cnzGYzysrKoNPp0NzcDMBvOMNxHBiWg5QCWI4Dw7KQILTonKzWR0dHUVxcHLYuzrAcnF4GH3VOIFkth0ImwaTLh486zdh0So6k1Wr9/gvZ/qEC0vEmdeKBgQG43W4oFIoAIv7yikwYMrSYdPqgYJ1gxtuBzEysXbt2yg0tUsNuNkQsvCmFinz3er0otNuRlTiGxh4LlPDhvHxgoLvdX6dUqKGQAiaHF3KpBFY3jbNKktBrdmHc5oVWJcWkk8aKnASo5RJMLFB0jtXN4B3jOLISlZCeMin6oHMCF1emIT1G0fJCROOlm56eDolEgrIycdI/MYkRQuzatQuXXnqpqOcWiyVBuqOjo7wCoL6+ftbkBszOLtJsNqOtrQ1arRarV6/GZ599FtNkYTEQOqIVFhby5Qyv18sTj1Ypw6o8PY70WkBRHGiGxYrcRLzbZkK3yYXSdC0uqc6AhPKbOHd3dyMnJwdr166d9v30Tbhw3ysn0W1yQq+W4wsVqcg89cFMUssxbPOAZlnIQvx+QCx3ejo+7pnEpMOL3EQ5ktUsbDYbRkdHeRct1ucDp1Tykr9QxySmYTdTIo6UzEuMaL68LgVfPpVrSMItbTYbrOMjyKXt6LQw8MkUqMpKRL6awffOy8crx8YwYvXi3LJEfHVVFt9Im83QwUzhZVhI8Ln7m4SiIAHgZebG3EIs6VqtVtFkSxApMUKI5557Dh9//DEOHDgQ1WtEwmlPularFaOjo6iurkZvb29MCBeYGenabDYYjUZIJBIsW7YsoDHAMMysVt6AOP2w0KQnIyNjSnlF+Bwcx2FlbgLSNDJY3T7oVHLs+rAXDd0TvJTsI+MIsqU2uCgVqgoLsSIrY1qiYVgOP/jbcYzaPdAqpbB7aPzj6BBK0rRIUsth99BIUMpCEm7we/jNvzuw32gCB/+2+5ZzCvGlFcXw+Xzo6OiA1WpFUVERWJbF8PAwOjo6pqgNEhISZqScCLUiJr8nHOyYSaM1ONyyCsB5Qb4TNpsNdSoaqiQVdDoZ7JNmUAkJYBgmJgnV0SJFq0COXoVBqxt6lQxWN42MBCXvgxxrRJOPFq3ZTaTECIK3334bDz30EA4cOBAzTiE47UlXr9dj+fLlAVNPsUA0RjWkXup2u2EwGKbIWOYrsod42+p0OqxZsybkxUJIl2EYnlhyk9XIozToNbtwuGcSSWo5OI6F0+XCO20eXL4sAyWZieizeLHns2FcvSYnJHGO270wOXzQKPyXlVohBbx+E5eiVA2UMgkuMER2RmsbdeBAmwl6tQwSyt/x/8MHvajSeTA6PIiioiJUVFRMITzhKnJwcBB2ux0sy05RToS6+U1HxOR5yYSd8N98Pl/ATSwWdWKC4OGCwcFB2Gw2yOVyWK3WABnVXNd5ZRIKt51fiJeaBtE94cay7ARsWZMzIwtOMYi0gyCYiWRMmBiRm5uL3bt34/nnnw94zNGjR3HLLbdg3759ERtzM8FpT7pzlR4hxpLR6/Wio6MDk5OT0w5akOeKBelOt9J1OBwwGo28t+10AxaENDweD4xGIxITE6HX6/npNy/DgqIAt8sFhmUhVyhAeWhkJvkJMyNBgSGLGxYXjVTt1FVOgkrGN32IQbmEAi5dnoGCZDW0Cpmo/DObh4b0lMwKAMAycDhdsDrdqK+vD9tkCaU2EPrKdnZ2gqZpqNVqnoQTExOnvUEJ/0uej6ZpdHV1YXJyEpWVlfzfNhZ1YoJQwwUdHR28GbnNZgvwJxbqWXU6XUxUN8KtuF4tx83nxE42FQvMZKUrJjFi27ZtsNvtuOqqqwAABQUF2LNnT8yO+7QnXQKy3YsVwpG4UPtbXFyMysrKsNvMmdg7hkIweRPSt1gsKC8vD2u1KOzm19fX85324eFhuFwu/0Qfy0HNujBJy6BTq+H0MdCr5bzHgz/lwb/yCQWNQoqtFxTjyf1dIId56bJM1OQkRrUNL0nT+BtLLh/AeODwcijPSsLKakPUMqXpfGVdLhesVismJyfR19cHj8cDlUoVQMTBygnSHO3q6kJ+fn6A7C9ceYKs3GZLxCzLQqFQIDk5OWBsXbjCHxoagt1uD9ATE0KOtry1EGqJaDDTqJ5IiRFvv/32rI8tHE570p2rbq5MJoPL5Qr4N5Zl0d/fj76+PuTm5orW/s7UyDwYZLBBqPmNRPqhhhtUKhVUKhXS09PBcRyOdQ7g8MkupCTqcPf52XjxUzP6LC5U66VYlatDx5AJapUSEokcawqTwoYdfq02B8uzE9Ex7kBmghJrCvRR/40SFBLcvFKNP3w8DicUqC3WY9vFpTHThVIUBY1GA41Gw0/gkVReopwYGhrib0ZEQzw2NsaXboJrqzNp2JHfE0vEQhI0jjrw/OEB2Dw01hcl48qVmdPqiYVx79GY0Cz21AibzTYj0l1onPakCwRaDcZqiky40hU2p9LT06PW/sayvGAymdDX1xdR8xtukozAYrHg3SMt+GQcyMrIwTCk8Pnk+MXXDf4wS58PVqsVrQNmDJmtkDIeqCZMaGkZ42ukWq12CmFUZukCYmvEgnj39vT0oCo/Hy/eWj3t37Jl2I5H32rDuN2L2jw97tno1//OFME3IwKn04m2tjaMjo5Cq9XCarXik08+CVgR63S6kKQ54aIxZvNCKZOgIMVvSB+8Iib/T64PjuOmdWIjrlpDFjceebMdEsrv1/DPT4fhY1hcW/95FLmYOjExoRH6TgjrxAtButG85kKGZs4GS4J0CQi5xUJWQ0iXeMomJiZO25wSe1yzgclkQmdnJxQKRdjYIDFk63a70d7eDq/Xi3FpKqqK1Xz67sCkC/2TLpSkaSGXy5GamoqzgkZjyWqwp6cHdrs9YAsfjoTCgYRs6vV61NXVhd0Kj9k9uP2lY3D7WMhlEuxvG4fF7cNvr14R1WuGg/AGUFhYiJqaGv480jQNu90Oq9WKvr4+ftRZqJwwe6XY2zwODv5hgrJ0DS5dlgnpDBp2pDxB/q15yA4vw/JSPKmEwvsd5gDSDYXpTGhIsCVZFROPXKVSCY/HA4vFErM6cSSIVS7EspQ431gSpCu0d4zWAHk6uN1ujIyMwOv1YsWKFdBqtTN+rtmQrtDbtri4mB8WCEbw6ikU2dI0je7ubphMJt4B7LODfQHbdurUxNF0kMlkUwxLGIbhiVhIQsFEHOpD63a70dbWBpqm+YDLSPhswOqvP58y+5bKpTjSZ4GHZqCUzZ4YrFYrWltbkZiYGPIGIJPJkJSUFNA5Z1mWJ+Lh4WH87TMTwHFI1CihVqtxvNeFygw1yjKnbodDNezIc5K/6djYmN+aUiqFBCw4luOJh2ZmFllPECrYkmEYDA4N4eO2QbR/0g0540aejoJOkDA8kzpxJERLunE/3QUGMb2ZaZ4Z8Pl20u12Q6PRYNWqVbM+LqlUGjLSPRzIalTobWsymQJSigmCR15DfXgHBwfR19eH/Px81NfX849ZkZuAg50TSNbITzlzSZGVGN1qXiqVTiEh0twhk2VEvqXT6ZCYmAitVss7ShHlh1ho5NKAmwt7qrkXSf8bCT6fjz/nlZWVUXm1SiSSAE/Z9LFupGjkoH1euN1uuC12nGhuwVgnyysnSImG+DSEek6Px8PfdOvr6yGXy7GuRIXXm8cxOOn33aUAXF+fDa/XG5OGHeD/m342RuPYpBS5GclwgUWCToPqfDWfGjGTOnEkiN2p2u3209JLF1iCpDvThpVQ/kX8BD755JOYHFdwpHs4kNXo6OgoSkpKArxtgyVjYkoJ4+Pj6OjoQEpKSki5VW2+HnIphc5xJzISlKgr1M8okSIY08m3iGNXR0cHZDK/mfjQ0BAcDkdYHa0QdYVJMGTqcHLIBpr1+8Pecm4hPzEVLTiOw8DAAPr6+lBUVBRRjSIGFZlaHB+0ISNBAQmkyEhX4YK1eUhUyeB2u2G1WmGxWNDf3w+32w2lUhkw1KFSqdDb24uRkREYDIaAVWiCWoEHN1fh/XYT7B4Gy7J1MGRoRQ12iCVip5dBy6gLmTo5UnUKcByHjnEX1hYlIzs7dMKwmDpxJIj1O7FYLAGm6acTlgTpivXUDQVCciMjIygpKeE/cESPGQuIKS8IjXry8vKwfv36KRcpeR4xZEvM0eVyeYADWDAkFIWaXD1qcue+C0yikbRaLc4++2woFIoAHS3xqiAOZEKDdCERy6USPHH1CrxxYhRjdg+W5yRiffHMYrgtFgtaW1uRnJwcVgMcLc4pS4WEotA25oBOIcMl1Rm86oPUVYUho0LlRH9/PywWCxQKBdLT03k/CmHTUquU4ZJlgSGl4SbsomnYAf7pQo5lIT2lq+alcUG1VLF1YofDIUpPHM002umoXACWCOkSRLPSFXoThLJ+jKXuNxzpchyH8fFxtLW1ITU1NaxRD0VR8Pl88Pl8AQJ8IaJxAJsPHO2z4LF/tWHU4kSpXoKffHkZctM/J0hhE46MY3IcxxPx+Pg4urq64PP5phDxFStnHgTp9XrR1tYGj8cjupYcDRRSCS4wpOECg7iyCSkxjIyMQCqVYsOGDfwQhM1mQ3d39xTiClcrDzdh5/RmDiD3AAAgAElEQVT48H/HRtE64kCKRo4ratL5phxZDWvkFLJ1MvRbvFB5aNg9DLL1yrBywYD3P02dOJKeeKmnRgBLhHSjWelyHIfh4WF0dnYiMzNzxtaP0WA60rVYLDAajVAqlaitrZ12NUpWKQqF32P10KFDvH6U1BGVSiX6+vowMjKC4uJiFJcZ0DHuRLfNgpI07azkVDNFv9mJH/7zGBiaRqJGiW4nhSc+GMKjXwm/KiUeCjqdLsCBjAw0TExMoKenB16vd0p9NFI9n2itBwYGUFJSgoyMjAVvxgjLG8HHFIq4CBEH18qF5Ylwo85/+2QEn/ZbkKpVYMDqxR8ODuLui4qhVUgD+gMrUznolUp45RSKkrVYXaCfcQkHmL7kJNQTj4+Pg2XZKakRwXXi0zU1AlgipEsgl8vhdrun/TlZURJZUqyNLKZDMOkSrwaPx4OKioqwtSnhh4Ck8wLgNbRWqxW9vb2w2+1QKpVIT0+H3e3DrrfbYHb5x3oTlDL85/nFSNPNj1kKWb3/30EjWJZDqj4BFAUo5Bw+HbD6rSSj/PBON9AgrI8GT5YJiZiiKN6bIjU1FStX18HiZmDz0EhUxbYDHw1sNhtaWlqQmJgoqrwRqmlJSjTE/ImUaNRqdYDnhFKphJdh8Vm/FTmnkiJUcimGLB4M2XyoyvLfsJxOJ1paWqBSqbBxVRGkUim/Svb5fDGbsANCp0YQog0VapmQkICOjg4YjcYZNdIipUZ4PB5cf/31aGpqQmpqKl588UUUFRXN+P2FwpIi3elGd8mKUqFQYOXKlVFFfMRi2IIcF/G2NZlMKC8vR1paGkwOL/Z8OgSXj0F1diKWn8rDilS3lcvlkEgkGBsbQ1JSEmprawH4P8RvHh9Cx9AkkuUsJFIphm1S/KORwTfWF4oKXJwNSC1ZoVBgRWUZXuvrAvxeYfAyHNRyKWaxWAqAsJ5I6qNkssxqtfKrQZfLBZ/PB6lUioKCAvjkCfjFvzpg9/hvhFfUZOG88ulHqOcCNE3zbmnRKiWCMd2oM1lBCncGCqUSLqcXVikNrVrlT4UAB4XU36QlzbtQadDROLHNlIhpmoZcLg9bJ37rrbfwxhtvYGBgAHv27EFNTQ1+97vfRWzAiUmN2LVrF5KTk9He3o7du3dj+/btMU2NAJYI6QrTI4TlBYfDwWtAI60oQ4GQ5Wy1iBRFwel04tChQwHetpNOH/7a0AeG5aCQSdA6MggvnYFVefqwTTIia+M4bko9MjU1FcpEDzLTpEjXKcCwLKRWJ8x2D9rb2+F0OiGXy6ek+M6WiMkNxWq1wmAwQK/Xg2E51LaYcaTPAnD+93LPxtI5JX3hZFlaWhp6e3vh8XhQXl7OO3TtPHASdrcPiSoppHIFXmjoQo6OQmlW8pwdm5dm0W1y+muYjB39vd1T/BtiCaFJfPDO4EvsIF45NgbGZIePZlCaLIN9qAMftVqRlpaGurq6GVtiRtuwC0a4RhqpE992222w2+2oqanB5ZdfjpaWFlGKBzGpEa+++ip27NgBAPja176GrVu3xjwrcUmQLgFppJFmktVqjWgEEw6zJV0yPtzR0QGWZafUj7tNDri8NHKTNQDHQU4BBzvNqDm12g3+QxNiI/HxwlqfEJWZOnzYMQEPzUJKAW5Oikuq87Dy1GqOJN+S7ajL5YJMJpsRERPVRX9/P4qCst+kEgo7vlSBxq5JTLp8qMjUoSw9tg2r6UAmCTMyMlBfXw+pVIrjg1Z02DUYZ1RYXpAGjuPg9XphmXDimLEb4z1GPg5GeB5ma/ri8NB4Yn8X+swO2G02pGvl+OHmlUhJiD5UcTYgO4Mv1ZWioiATfRMuaOUSqJ3DcNisSE9Ph8fjweHDh/ltPvmabsowXMNOONwh1ihe7BgwqelqtVqsWbNG1PsXkxohfAzJyDOZTFHpyCNhSZBucIG9qakpJjHrs3EHE3rb1tXVoampacodXHJK2M+xLDhwYDgWMqkk5HBDX18fBgcHA1bK06E6OwFfrc3CmyfGwHAcvliZjrNLPyfoUMm3wUQsXBETEgomYpKQkZqaOm09UiaRBLz2XMPtdsNoNPobQStX8s3JVz8dxrMHe+H2sRize9A/4cL55SnwclJQChXqawzIS1bD5/Px56GrqwsOhyOAgMhgRzRE/K+TY2gbNCFB4kNxVjIm3MB7HRZcuWp+SVeI8gwdkiVutLe3ISUvDyuWBfpckHFvm82G3t5eXmdOhlvEmMSHuo4jRScRj+JIsFqtUTfSxKRGRJMsMVMsCdJlWRbd3d3o7+8HgJAa15lgJu5gYr1tAaA4TYNElRSDky7IZRK4fSy+siqb/zkZ/yQpEKEywEKBoiicU5qKs0tS+O8jIRIRj4yM8ESsVvunkmQyGVasWDGjGOxYg2VZ9PT0YGRkZMruxkMz+EtDH6RSCi4XA41CCrPDi9eOjUIplyIzQYFXPh3CLecW8bHywl2EkICEfhPBBBTqmjObzTh6sh0qmRKZ6Zn+1Sbjw5jdOy/nJRTIlBvgT74N1VCebtxb2Nwi17n21GgwORfT7QzDlScYhkF/fz9omubJF5h+RTxXqRHkMXl5eaBpGhaLZdod5UyxJEiXkMr69etx6NChmHmARmOMHq23LcuyUEmBb6zNw6f9FnhoDmXpWpSc2n5bLBa0tbVBo9FM+8GIhNneoYOJmKZptLe3w2QyISkpCTRN49NPP424Ip5rjI+Po729HVlZWSHz21w+FhwAq8sHmYSCVCaBy8dCKgHK0zXI1qvwcY8FVdkmXFQxNdY+nN+EzWZDf39/gOkN8eIdGhoCy7I4t6YU/zw27ve04DjYPDTKM+anzCIEx3H8OHhpaWlAk0oMwkm+rFYrv0AgmmpheSLcqLPD4cDJkyeh1+uxdu3agEbydA27kZGROUmN2Lx5M/7yl79gw4YN+Pvf/44vfOEL8ZVuKEgkkpjLOgBxpBuNt23wRURRFJI0Cpxv+PziFzqAVVRULIr5cqHjVn5+/pSoHK/Xy6sFhCtiQsSJiYlQq9Uxv3hdLhfvS7Bq1appNbp6lQwlaRoc6p6AXErB5/M3fDRyGWRSf7ddIZOgf8IV8vdDYTq/CbIdN5lMUCgUkEqlyJCasCpdgiND/t3BhYY0nFs2v2oJh8OBlpYWvtwVK236dBaSLpcLNpstwCSejDoLPSeItryysnLKIE+oOrHb7cbjjz+Ovr6+qBciYlIjvv3tb+O6667jeya7d++exdkJDSrC1NVp45/m9Xr9QYoffYQNGzbE5APe09MDqVSKvLy8KT8jRNTV1YWcnBwUFBSE9bZtaGhAaWkpEhMTIZPJIjqApaamLrhoH/BP/hBry5KSEtFNRSERW63WmBIxwzDo7u7G+Pg4ysvLRW3/Jpxe/PT/WtHUZ0GiSgatQgqTw4fa/EQoZBIMWzz45oY8XGiIbvUnhNVqRUtLC5KTk1FSUsLrW4mG1jRpgd1mgwSc6C35bEFKb+Pj46ioqFiwCUWhSTyRsU1OTvKjzuSaCNe4/OSTT3DHHXdg8+bNuPfee+fsnMUI017YS450Dx06hNra2pj8QQYGBuDz+aasok0mE4xGI5KSklBaWhrW25asbE0mE0ZHR/nRR7INTUxMhMVi4bumOTk5iyIiRWi5aDAYYjImS4iYkLHT6YRCoQiYrAtHxMIad05ODvLy8qI+V8cHrfi03wqK8huhD1jcAAesLUrCt88umJFTGUkottvtqKysDFvHBwK35ORc0DQ9hYhnm/w7OTmJ1tZWZGRkoLCwcFFcV8KbQFVVFVQqFX8ObDYbP+pMyhJDQ0MoKyvDzp07sX//fjzzzDP8gNAix9InXZ/PB5ZlcfToUVRWVk47UhsNRkZGYLPZUFZWBuDziHWpVAqDwRC2gRRstygkEuK2NTQ0hOHhYV5bSj5wer0+6g55rEDKJaOjo1FbLs4EYonY6XSitbUVSqUSZWVlMZkmZDkOYzYvpBIKqVp51KtuIgns6upCYWEhsrOzZ7w7IcMMwt2BsDYq3JJHAqm9O51OVFZWLopGJ/D5TiA9PT3sTYCYxNtsNmzbtg1NTU0AgIsuuggXXXQRvvnNb87nYc8U014IS6KmKwTxX4gF6ZKabihv2+kgxgHM6XSio6PD7426bh3UanWAEbiwQy7cjmu12jkrOZDQRbKKDNWQmgsoFAqkpaUFkLuQiIeGhmCxWMCyLNLT05GamhpwMwuFcbsXTi+DLL0SijAx4RKKQmaU3sEEDocDra2tUKlUEZMuxEA4zBDJb0KlUgU0LoVNKjIGXFhYGDKmvnXEjl6zE8kaBVblJ87ag1gMGIZBV1cXJiYmUF1dHXEnIJPJoFar8d///d8wmUx48803UV5ejubmZoyNjc358c41lsxKl6ZpMAzD30lnOhAhhNlsRktLCwCgtLQ0rDmKGLKN1gGMpmmefEhdlIj3hTWw2RKxzWZDa2srtFpt2HLJfEK4iszLy0NGRgZ/U7JarXC5XFAoFAGDDCqVCn9p6Mcrnw1DQlFI08rx882VyEqcual9MIT15Eg34LkAmSoTnguPxwO5XA6PxwOFQsE3YIOvi3dax/BS0+Ap43cOq3ITcct5RTEL/AwFUuLIyspCQUGBqGu1qakJ3//+93HVVVfh7rvvnnNDqjnC0i8vENJtb29HQkJCgFdptCBTVl1dXZDJZGF1v2LIlmEYfqa9uLh4Vs5WQqMbQsSEfMiXWOd+r9eL9vZ2uFwuGAyGRaGUAD6PKFKr1SgrK5v2JiBcEVutVnw66MBzLTSS1DIo5DLYvByqshPxi69Uh/z9aEGm3LKzs5Gfn78oaqQcx/EWpeSat1qtfKwTL+PTJeCHr3UgRauAXOq3LR2yenDXF0vnZEqQfBbtdjuqqqpElTjcbjceeeQRHDx4EM888wyWLVsW8+OaR5w55YVg/4VoQBo17e3tSEtLw+rVq9Ha2hrywyVskk2XSUZsJLu7u2O2ZSdhkcFDDIR4BgcH+SSCYCImIBNuROa2GOwNgUATGOLfEA7BpYleyTAUXd1QKCRgaBpSlsaxnlE0NbkCtuPRqiaEU27hpGnzDbvdzutb161bN0U9IzRG7xscxrjZArgkUCgVUCgU4FjA65t9SnUwzGYzjEYj8vLyRHtLHD58GHfeeSe2bNmC/fv3n66rW1FYMu9sNukRQGhvW5qmQ+p0I2WSAf4xYLLqXrNmzZxu2UPVRYnlIUkiIJaHMpkMFosFmZmZvCfBQkOoAy4oKJixCUxWohJSCQWZVAaFXA4350N1jhbLl5fxDaqhoaGA0kS43QHx3h0cHJyXpqJYkBqp2WxGZWXltEZOSqUSSqUSaWlpKAFwjrULxwcsUMkAk90DsDSGO07AMSALaFzO1G+Cpmm0tbXB5XIFjGCHg8vlwsMPP4zDhw/jueeeQ1VVVdSve7phyZQXGIYBTdMYHR3lp8LEIJy3LcdxOHjwIM466yz+ezFNMuIAVl5eHvNEgpmC+LYC/qkpp9MJr9fLpzGQr/nWPpJ6sk6nQ2lp6axen+M4PP1+N95sHoOEoqBXy/Dg5irkJk1dmQrtH4NrxImJiaAoCl1dXUhNTUVxcfGiuDkB/pt5a2vrjEocDi+Nvx8ZROuIA+k6BbbU5SJHr+L9Jsi5EMq2yO5gOsMbAuJVHY2Ko7GxEXfffTeuvfZa3HHHHUttdbv0a7osy8Ln82FiYgLDw8MR75jEsctsNvOrmFAXChm2mI5sfQyLPZ8No7HLDK/LgXXpDDbVVcZ8XnumCGW5SCCUKZEvohcVEvFcfBiE2tZYT94NW91weBjkJauiimT3eDy8SsDlckEulwcoBaKpl8caPp+PXxzEShIZDkK/CavVCrvdDoqiphAxy7IwGo3w+XyoqqoSJWlzuVx48MEHceTIEfz+979HRUXFnL6XBcKZU9ONVF4gRs0DAwMRHbvIytZms0GlUvEGzUK8fmwY+z7tg5pzQ6VNQKNFiw2cCgtNuULLxene53QypVApBMJhjuncpcSAzP/39vaiqKgopKxptpiJWoHjOJhMJvT09KCoqAhZWVmgKIpfERP5mtjSRKwgVHEUFxcjMzNzXkhfjN/ExMQEPB4P9Ho9MjIyeIvQcNfGwYMHsW3bNlx33XV47LHHFs0OYj6xZFa6xBvV7XajubkZq1evnvLzkZER3rGrqKho2hWcsEk2MDCAsbExuN3uKasei8WCB15vgUalRnpqEiiKwuCkG5tXZuFCkYGEcwGh5WK49ykWwlFWsiVnWTagDjidy5YQpG4+xqjx3hAFl4/FhpIUfLU2O6yedq5B1BJEMhepxCEkYpvNNmdE7HK50NLSAoVCAYPBsGjGXr1eL1paWkBRFMrLywMaucGZbRqNBlKpFCqVCj/72c/w2Wef4fe//z0MBsNCv425xpm90hV6265ZsybsFii4SZaXl4e8vDx+dtxisWBkZATHjx8HACQqlXAy4DWSLMdBp1iYuzepJwMIG7seLYRjmbm5uQA+n6ojjTrishVqqk4oTUvILsYz+/uhkkmhkEmw9/gIAOCautyYHGs0YBgGnZ2dmJiYiMqXgGTRCV26hERMFCQzJWIiAxscHITBYFg0pSrhqpvo1gHwixEC4U36+PHj2LZtG8bGxlBQUIAtW7bA5RJvLLQUseRIVxgCSbxtSaxNuEmYSE0y8v9jY2Pwer2oq6vzp9UOmPG797rRM2aDz+dDuhqQWoDeXhv0er2oFeBsQdM0P/ETLlEilpBIJFNs/kJN1REFSGZmJgwGAw72uUCzHJ9OnKZT4mCned5Jl0gDSVZWNKvSHrMTxwasUMqkWF+cjASVTDQRC522QhExaXgmJycvGnUJ4H8vJ0+ehFwujziBR27SEokEb7zxBrKysvDPf/4TNE3jyJEjGBoawsqVK+fx6BcXlkx5AfBfGADwwQcfIDU1NSpv23CKBOIANj4+jtLS0ilNt3G7F90mJ+RSChUZWnjdgWYmwgYEWQHGoi4XbLmYm5u7KPS2gH8SiZgCpaSkwG63w2q1orHXhr1dNLL1SsjlcnhZCVJ0Kjx0xfxIhYR2kAaDIWoPh+YhGx56wwia5cAByExQ4qErKkUnCguJmAwxKJVKXlHi8XhQXV29aAZVyDXW29srWjbHcRw++OADbN++HTfddBNuvfXWObl53HjjjXjttdeQkZHB7zyDj+OOO+7A3r17odFo8Oyzz04pO84hlr56AfB/oLq7u9He3o7ly5eHla6IIVuO4zAwMMA7yefm5s5o1UpWgBaLhZfkEEPomdocztRyca7h8XjQ1tYGn88X0p3M5WPw4N5WdI3ZwTIMOJbGlSUSGNLmViVAGqjDw8Ozys2775WTGLS4eJIdtnpww4Z8XL585hOQw8PDaG9v58+VcLhFOOI83zdUl8uFkydPQq1Wo7y8XFRvwG6346c//SmMRiN+//vfo7S0dM6O77333oNOp8P1118fknT37t2LJ554Anv37kVjYyPuuOOOKZloc4gzo6Z79OhRpKSkQKfT8d3nYIiZJAP8I5/t7e1ISUmZtaFJKMNr4Tjv8PAwXC4X/0EjZBxqFUbMd3w+H6qrqxeNDliY40ZSCUKdV7Vcih9fVoGmnkm4fAwqMhNQkKKeYnIjPB/ka7r0gUgg8//p6emzngp0emnIBU0/CeX/t5nA6/XCaDSCpmnU1dUFTLoJ/RWCpwznmog5jkN/fz8GBgZE15Q5jsP777+Pe++9F9/5znfw5JNPznlZ7bzzzkN3d/e0P3/11Vdx/fXXg6IorF+/HpOTkxgaGuKVOguFJUW6dXV14DgO4+PjoGl6yhSYmEkyu92OtrY2yGSymDajghFqnJdMkVksFvT29gYML+h0OkxOTvIm59FGrcwliFoiLS1NVI6bWi7FOUHJCdFM1RES1uv1YSf9vF4vr22NVZbb2aWp+NuRAUgoCj6GhYSisDI3OmNw4Xh4SUlJSJ8QEiMv/DuHI2JCxrMlYqfTiZMnT0Kn04muKdtsNtx///3o7OzEK6+8MicpLjNBqPTfgYGBOOnGEiRbiUSxkw+kmFICyTiz2+2i5v7nAuSDRrrCZHihr68PPT09kMlkkMlkGBkZgcvlmrVmdrYgngQsy87JDSrU+SBEPDk5OeXGJBzmIFrggsJiHJugcPDwCHL0KlyyLANq+czP13/UZoPhWLxnNEOrkeP/1efCkBneqlAIp9OJlpYWqNXqqHdQkYh4YGBgxkTMcRx6e3sxNDSEyspKUe5pHMfhwIEDuO+++3DrrbfiqaeeWhQmQATzkew7Eywp0iUgsrGZOICFyzibbwj1o2eddZZfknZKjmOxWDA4OAibzQYgtFRrriBM3p1PTwKKoqBWq6FWq/nVodBzlriAOZ1OKJVKZGVl4aXjE/h0yAWdUo6mXgtaRuzYdnHpjH1kpRIKX6/Lw9frpkY4hQOpKY+MjMTUEnI6IiZN3FBEHFyqIcY50SgmbDYbfvzjH6O3txd79uxBYWFhTN5PLCEm/XchsKRIV2h64/F4eLOaSA5g2dnZ82baLQZCXWvwiKxQM0sQSqol9N3V6/UxC4YkxJaZmbkozhlFUdBoNFAoFLBarZBKpairq4NEIsHA2AQOdQ0jUcbASwMqqQwn+txo7knAsoL0edshWCwWtLa2IjU1FfX19XN+zkLtEIReE0IiZlkWHo8HBoNh2lF4ITiOw/79+/HDH/4QW7duxTPPPLPg18B02Lx5M3bu3IlrrrkGjY2N0Ov1C15aAJaYesHn84GmaQwODqKrqyugKSXUy5LOf0JCAkpKShaFaTcQW8vF6Xx3hYqJaCwKXS4XjEYjKIqCwWBYNPaGxI6zo6NjimzO4vLhrn+cQGaCvyHp8/kwZHHhhhUaJMA1o6m6aECsKm02G6qqqhZN0xPwe+42NzdDq9VCrVbDZrNFXBFbrVb8+Mc/xsDAAJ555hkUFBQs6Hv4+te/jv3792N8fByZmZl44IEH+MGo7373u+A4Dlu3bsW+ffug0Wjw5z//GXV1dfN1eGeGZGzbtm18xHRtbS0oiuKlWmQbTtM0ZDIZysrKFk3iLmn+dXR0IDMzM2yy8GxAVjtEuubxeKBWqwNuTsE1xpkk784XyJisXC6HwWAI2Th95oMeNHZNQqeUwuljUJKqwT0byyCXSgKm6sgIKxCbUg25ERCp4WK4zgD/jZ3YQlZVVU2JTg8ecXa73di5cycUCgUaGhqwdetW3HnnnYtmaGMR48wg3dbWVjQ0NKCxsRFHjhyB1+vF8uXLUVVVhaamJpx77rnYuHEjOI6DxWLha3/kAxapGz4XsNvtMBqNUCgUKCsrm9cVpLAeSsiYYRjeZYxlWQwPDyMnJ2fRJCUAgTXlSJImL8PireZRdIw5kZOkwmXLM6BVTF9VE5ZqCBFHk1Xn8XjQ2toKAKioqIhJgGasYLFY0NLSwt/Yxfw9JycnsX37dgwNDWH58uVoa2uDw+HA/v375/6AT2+cGaQbDIfDgfvvvx+7d+/G8uXLMTIyAo1GgzVr1qCurg51dXXIysoKGFzwer086ZDV31zc1cNZLi4kyKq7vb0dLMtCKpUGTNQR+dpCETBJJcjMzAxIlB20uPF/nw3D7qGxvjgFZ5Ukx2x1SWwOCRGT4RYhEavV6oDJrcUk6SMeExaLRXSZg+M4/Otf/8L999+PO++8E9dff/2c/c337duHO+64AwzD4KabbsK9994b8PPe3l5885vfxOTkJBiGwaOPPorLLrtsTo4lhjgzSZfjOOzatQvXXnstNBoNOI6D2WzG4cOH0dDQgMOHD6Onp4efv1+zZg1viENWfjabDRzHISEhgSdhnU434w90sOXibGK7Yw1hIkF5eTlv68cwDOx2O39jIo064TmJRUBmOAgHCSoqKgLkaWM2D360pwUuHwO5VAKXj8GNG/JxcVXGnB2PsGZuNpthsVggk8mQmZmJpKSkBfXeFYKYnpPdipjjmZycxH333Qez2Yynn36aNzmaCzAMA4PBgH/961/85/CFF15AdfXnuXbf+c53UFtbi1tvvRXNzc247LLLwg5FLBKcGRNpwaAoCjfddFPA96mpqbjkkktwySWXAPCTYHd3NxobG7F//3489thjfOODrIhXrFjBT0x1d3fD4XBAJpMFlCXETEsJLRfr6+sXjVO+MH49Ly+P7/4TkJFl4WpcmFTc3t4+JSBT7DkRc2xkFFvobCVEU+8k7B6a99FVSiV4/fjonJKuXC5HcnIyLBYLaJrGmjVroFar52yqLlrQNM3/XcRG53AchzfffBM7duzA3XffjW984xtzvqM5dOgQysrKUFJSAgC45ppr8OqrrwaQLkVRsFqtAPwlksUg+5oNFsenfgEhkUhQUlKCkpISfP3rXwfgX8UcO3YMjY2N+Mtf/oLPPvsMMpkMq1evxurVq1FXV4eioiJ+9Uemg6ZrSs2V5WIsQGrKKpUqqiw3mUyGlJSUgHqq1+vlV8PknKhUqgDFRDQ1c6vVitbWViQlJYWddJsiB0SYZUaMQEaLMzIyAmRgoabqSPkq1FTddOPeswGR9eXn54s2iZ+YmMC9994Lq9WKffv2zRuxhZoaC/ZH2LFjBzZu3IgnnngCDocDb7/99rwc21zhjCfdUJDL5TzB3nrrreA4DjabDR9//DEaGxvx85//HO3t7cjIyOBXw2vWrIFer4fVasX4+Dg6OztB0zQ/elxUVDRjw5y5AE3TfJ0vVjVlhUIRYG8onCAzm83o7u6Gz+cLqJknJCRMWfEHS63CWXICwJqCJLx8dAhjdg/kEgncNIOr1syNnImsIB0Oh6jR4uDhBbFTdTPx+hBG+ohNLeY4Dm+88QYeeOABbN++Hddee+28XqNipsZeeOEF3HDDDbjrrrtw8OBBXHfddTh+/Pii+SxFiyVd051LkNiZxsZGNDY24tChQ7ysavXq1aPjPrYAABS5SURBVJiYmIDdbsd//ud/QqVS8RIc0gmfr1poqOMmQyELYQcpjAMiX0K9LE3TGBoaQmFhIXJyckQf25DFjdeOjcDupbGhOBnrimLXSCMg8UWxrsUHq0isVmvAzUlMVh3xBxZGDUWC2WzG9u3b4XK58OSTTy7I4MDBgwexY8cOvPnmmwCARx55BABw33338Y9ZtmwZ9u3bx6+IS0pK0NDQELLUtIhwZjbS5hsMw2D37t3YsWMHkpKSIJPJ4PV6UVNTw6slysvL+TDI+ZatkeRdrVaLsrKyRWMHybIsr2vlOA4SiWSKOiBWHsQzgdvtDvDgnQ9ZYfDNyWaz8XI+4cAPwzAwGo1gGAaVlZWiShUcx+H111/Hz3/+c/zwhz/ENddcs2DnlqZpGAwG/Pvf/0Zubi7q6+vx/PPPY9myZfxjLr30UmzZsgU33HADTp48iYsuuggDAwML3qSMgDjpzhf++c9/orq6GhUVFfwKpqmpCYcOHUJjYyNaWlqg1+uxZs0a1NfXo66uDmlpabwkyWKxxFy2RpJ3bTbblJj5hQYR64+Pjwd4EhCZltCDWC6XB5wTMeqAN5tH8ezBPnhoFhca0nDLuYVQyMRtS4UWh7Px4I0VgrPqzGYz3G439Ho9MjMzeWVNuGvFZDJh27ZtoGkaTz75ZEiHs/nG3r178f3vfx8Mw+DGG2/Ej370I9x///2oq6vD5s2b0dzcjJtvvplPJP7lL3+JjRs3LvRhR0KcdBcLiA5WWJYYGBhAUVERvxqura2FXC4PKVsjpCNGtiZM3l1s8jTg84ZPVlaWKLE+UZAQIg4OCw3eJXzSZ8FPXmuBTiGDTEJhwuXDV1Zm4dtnRzZnISYwer0epaWli2oCy+PxoKWlBVKpFGVlZQFexMEGSERDLJPJsGfPHjz88MP40Y9+hC1btiyqa2EJIk66ixksy6K9vZ0n4aamJjidTixbtown4urqal4dYLFYpsjWgld+pPO/2JIlgM+ntjiOQ0VFxYyn8IRhoYR0hLuE1zvc2NcyiVSdf8vt9jFIVMvw+/+3atrnFGqVKysrF9WuQFiPDzeAIZyqm5iYwI033sjHo99+++24+OKLUVU1P/FIZzDipHu6wev14pNPPuGJ+Pjx41CpVKitreWJOD8/P6AsQQxLiK2lWF/U+YIw5XaujNiJB7HFYsErnw7jH81W6BUUpFIpXAyFsgwtHr+qJuSqmgwSZGdnL6qxZ8BfVz558iSUSiXKy8tF3UQ5jsMrr7yCRx99FNu2bUNRURGampowOTmJBx54YB6O+oxGnHRPd3Ach8nJSRw+fBiNjY04fPgwOjs7kZuby8vbjh49iuzsbJx99tm8oJxhGOh0ugCJ1kKQCbE3TElJQXFx8bxs1x0eGne/3IyBCb+jmJTicOtqLZIl7oDRZo1Gg8HBQXi9XlRWVi4qHTUZDunv74+qrjw6Ooq77roLcrkcTzzxxJyOJUca4wWAl156CTt27ABFUVi5ciWef/75OTueRYI46S5FECvIv/71r3jqqaeQlZUFjuNQVlbGN+pqamrAMAy/GibNCGEddC5laz6fj5+MqqioiKi5jTVcPgaHuifhpVmsyE3gp9bIORkYGMDY2BhkMlnAIIder1/wMV4SDKnRaFBWViZqgpHjOLz88sv45S9/iR07duCrX/3qnL4HMWO8bW1tuPrqq/HOO+8gOTkZo6Oji13uFQucmWPASx0SiQSFhYVwu9149913UVFRAZqmceLECTQ0NOCFF17A9u3bQVEUVq1axQ9ylJaW8l1w4QgvkazFYkpKWH8sKipasEQOtVyK88unrg69Xi+6u7uhUChwzjnnQC6X834KFoslqrDQWENYhqmoqOA9MCJhZGQEd911F9RqNd599915SfQQM8b7hz/8Abfddhv/Ps4Awg2L026lG2kr4/F4cP3116OpqQmpqal48cUXF01Q3kKA4zjY7XY0NTXxZQmj0YjU1FTe4Gft2rVITk4OsHgMlq2FmhybDg6HAy0tLfwKbTE18YSEJibpVhgWShp1ZHqMnJdYvj+Hw8GrJkpKSkSVYViWxT/+8Q889thj+NnPfoYrr7xy3m5wf//737Fv3z788Y9/BAD8z//8DxobG7Fz507+MVdeeSUMBgM+/PBDMAyDHTt28N4nSxhLY6XLMAxuu+22gK3M5s2bA+6qu3btQnJyMtrb27F7925s374dL7744gIe9cKC1C4vuOACXHDBBQA+X4UeOnQIDQ0N2LVrF4aHhwPKEqtWrYJEIoHVasXIyAja2tqmyNaCDb6Fnf+KiopFY1dJYLPZ0NLSElUW2HRhoVarlR/oENbNZxoWynEc7xFcWVkp+twNDw/jzjvvREJCAvbv3z/vWmIxY7w0TaOtrQ379+9Hf38/zj33XBw/fnxRNXnnE6cV6YrZyrz66qvYsWMHAOBrX/satm7dykeux+EHRVHIzs7GFVdcgSuuuAIA+MmmhoYG/hx6vV6sWLGCJ+LKykq43W5YLJaALDa9Xg+KojA2Nobc3NwpLmULDeInOzk5KcrLIRwoioJWq4VWq+XHZsOFhZKyRLgECqIJTklJEZ2hxrIsXnrpJfzmN7/Bgw8+iM2bNy/INS4m/DEvLw/r16+HXC5HcXExKioq0NbWhvr6+vk+3EWB04p0xTgSCR8jk8mg1+thMpnmLbH2dIVUKkVVVRWqqqrwrW99C4B/a3306FE0NDTgiSeewIkTJ6DT6QJM4D0eD5qamlBYWAilUonBwUGYzeaA+vBClhfIAAa5GcwFMUUKCyV2oMFhoUqlEj09PRgfH0dVVVXA74fD8PAw7rjjDqSkpODAgQMLGqFUX1+PtrY2dHV1ITc3F7t3756iTLjyyit505rx8XEYjUZ+4XQm4rQiXTFbmcWadX86QqVSYcOGDdiwYQMA/7k1mUw4fPgwPvroIzzyyCMYHx/H2rVr+frw6tWreV9Zk8mEzs7OBZGtCU3PxTpuxRJSqRRJSUkBW2ih8fnAwAAsFguUSiUyMzPhcrkgl8vDHifLsti9ezd++9vf4uGHH8bll1++4Ne2TCbDzp07sWnTJn6Md9myZQFjvJs2bcJbb72F6upqSKVS/OpXv1rwkeqFxGnVSBPjSLRp0ybs2LEDGzZsAE3TyMrKwtjY2IJfnEsNDz30EHw+H+655x4MDQ3xY80ff/wx7HY7qqurA0zgaZrmm1E2m23OZGtC1URJScmsEpXnAqTuPTExgaqqKsjl8oCJOhIWKixLqFQqDA0N4Y477kB6ejoef/xx0YqGOBYMS0OnK8aR6Mknn8SxY8fw9NNPY/fu3Xj55Zfx0ksvzfg1I6klHn/8cfzxj3+ETCZDeno6/vSnP6GwMPJs/1KG1+vlTeAbGxtx7NgxyOVy1NbW8vXhoqIivg5K3NaEEfFk+x0NnE4nWlpaoFarF51qAvAbn7e0tCA7OxsFBQUhbwZCm0eLxYKdO3finXfegd1ux1e+8hVcf/31qKurm/eVexxRY2mQLhDZkcjtduO6667D0aNHkZKSgt27d8+4fiRG+P3uu+9i3bp10Gg0eOqpp7B///4zWi0RChzHwWq18ibwhw4d4uPmhfVhvV7PO4sR2ZpGowlIngglW2NZFr29vRgZGQlwKlssYBgG7e3tsNvtqKqqimh8TjA4OIjbb78dWVlZ+Pa3v43W1lYcOnQIW7duxfLly2N6jGKmygC/ROyqq67C4cOHUVdXF9NjWGJYOqQ7nxBTzhDi6NGj2Lp1Kz788MN5O8bTFWS8tbGxkQ8JNZlMMBgMfBLHqlV+Y5pQhuekUUdUF6mpqSguLl5Uqgng8/TivLw80YbxLMviueeew1NPPYVf/OIX2LRp04JPlQF+yd3ll18Or9eLnTt3xkk3PJaGTne+IUYtIcSuXbtw6aWXzsehnfagKAp5eXnIy8vDf/zHfwDwf/ibm5vR2NiIv//97/jRj34EjuMCTOANBgNcLhdftyVDHAzDYHR0dFGM7wKfa1NdLpfoYEjAL7m6/fbbkZ+fj/fee29etM5ipJgA8JOf/AT33HMPHnvssTk/pqWMOOmGQTRKiOeeew4ff/wxDhw4MNeHtWQhlUqxYsUKrFixAjfddBM/iEBM4H/1q1/xlpBWqxW33norvvKVryAzM5MvSwwNDU0JxNTr9fNa3yUytYKCAtHjzyzL4q9//SueeeYZ/OpXv8LFF188bzcOMYuLo0ePoq+vD1/60pfipDtLxEk3DMQIvwHg7bffxkMPPYQDBw7My2z+mQIyiHDeeefhvPPOAwB861vfgtlsxle/+lW0tbXhe9/7HgYHB1FcXBxgAq9QKGCz2WA2m9HV1RUQdUNM4GPtdObz+WA0GuHz+VBbWyv6Wujr68P3vvc9lJSU4P333593D99IiwuWZfGDH/wAzz777Dwe1dJFnHTDQIzw++jRo7jllluwb9++mBl5xJsa0+OnP/3pFC8NYgLf0NCAN954Aw8++CDcbneACXxNTQ1vAj8wMMDL1oT14dnI1khoZXFxMTIzM0Wvbp999ln84Q9/wK9//WtcdNFFi3KqzGaz4fjx4/wY+fDwMDZv3ow9e/acMdddLBFvpEVAJLXEF7/4RRw7dowfCS0oKMCePXtm/HrxpkZs4PF4eBP4w4cP8ybwq1ev5om4oKAAdrs9IIctWtma1+vlSx6VlZWiQyt7e3uxdetWGAwG/PKXv5x3y0shxEgxhbjgggvw2GOPxa+58Ig30maKyy67DJdddlnAv/3sZz/j///tt9+O6evFmxqxgVKpxLp167Bu3ToAn5vAk4DQl19+md/BEBJes2YNdDodXx/u7++Hx+MJKVvjOA4jIyPo6upCaWmp6F0Oy7LYtWsX/vznP+PXv/41vvCFLyx400/MVFkcsUOcdBcZ4k2NuQFFUUhOTsamTZuwadMmAJ/rexsaGvD+++/j8ccfh8ViQWVlJT/EsXLlSr5xNzo6ivb2djAMA5qmoVQqo9IFd3d3Y+vWraiursYHH3ywoKvbYERaXAixf//+eTiipYs46S4yxJsa8weJRIKioiIUFRXhmmuuAeBvhhET+P/93//Ftm3bIJFIUFtbi9WrV6Ovrw8cx+G6664DRVEYHByE0WjkzWxIfVgoW2MYBrt27cKzzz6L//qv/8L555+/4KvbOBYOcdJdZIg3NRYWcrkcq1atwqpVq/Dd736XN4Hfu3cvfvrTn0Iul0Mmk6GhoYGfpquvr0dKSgpfliCpE3/729/g8/lw9OhR1NfX48MPP4RWq13otxjHAmNxje/EEaCY8Hq92L17d0BNTa/XY3x8HN3d3eju7sb69etjQrj79u1DRUUFysrK8Oijj4Z8zEsvvYTq6mosW7YM11577axe73QBUThYLBY8/fTTOHbsGI4cOYLnnnsOZ599No4ePYqbb74Z5557Lm6//Xa88sorsFqtqKqqQk5ODoxGIyoqKtDa2opzzjkHHR0dC/2W4lhocBwX7iuOBcDrr7/OlZeXcyUlJdyDDz7IcRzH/eQnP+FeffXVKY89//zzucOHD8/q9Wia5kpKSriOjg7O4/FwNTU13IkTJwIeYzQauVWrVnFms5njOI4bGRmZ1WsuNdA0zZ04cYL705/+xN1yyy1cYWEhd9VVV3EOhyPgMTRNx/y133jjDc5gMHClpaXcI488MuXnv/71r7mqqipuxYoV3Be+8AWuu7s75scQxxRMy6txyVgcojwm7rnnHhgMBtx0000LcoynG7h5SiuJmzItWkz7x4+XF+IIqZgYGBgIeIzRaITRaMTZZ5+N9evXY9++ffN9mKcV5qtRJpQYKhQKXmIoxIUXXsg7m61fvx79/f3zcmxxhEa8kRZHPFzwNEbclOn0Q5x044iHC57GEHPDJIibMi0OxMsLcURUTAD+cMF3330XAOLhgosI0Zoy7dmzJ27KtMCIk24cAWOgVVVVuPrqq/kxUOIjsWnTJqSmpqK6uhoXXnhhzMIFI0nVent7ceGFF6K2thY1NTXYu3fvrF9zKUHMDZOYMu3ZsydmpkxxzALhpA3zLrKI44yCGKnazTffzP3ud7/jOI7jTpw4wRUWFi7AkS5uRJIYXnTRRVxGRga3cuVKbuXKldyXv/zlhTzcMwXT8mq8phvHgkGMuQ9FUbBarQAAi8UScut8pmO+TZnimB3ipBvHgkFM533Hjh3YuHEjnnjiCTgcjjiBxHHaI17TjWPBwInovL/wwgu44YYb0N/fj7179+K6664Dy7LzdYhxxBFzxEk3jgWDmM77rl27cPXVVwMANmzYALfbjfHx8Xk9zrlEpEaix+PBli1bUFZWhnXr1qG7u3v+DzKOmCJOunEsGMR03gsKCvDvf/8bAHDy5Em43W6kp6fP+rVvvPFGZGRkYPny5SF/znEcbr/9dpSVlaGmpgZHjhyZ9WsGg2EY3HbbbXjjjTfQ3NyMF154Ac3NzQGP2bVrF5KTk9He3o4f/OAH2L59e8yPI455Rrgu2wJ0/OI4wxCp837ixAnurLPO4mpqariVK1dyb775Zkxe98CBA1xTUxO3bNmyaY/rkksu4ViW5Q4ePMitXbs2Jq8rxEcffcRt3LiR//7hhx/mHn744YDHbNy4kfvoo484juM4n8/HpaamcizLxvxY4og5Zmx4E0ccSxYURRUBeI3juCnLXYqingGwn+O4F0593wrgAo7jhmL4+l8DcAnHcTed+v46AOs4jtsqeMzxU4/pP/V9x6nHLJ0ayxmGeHkhjjhCIxdAn+D7/lP/FkuEmtcNXgWJeUwcpxHipBtHHKExH2TXDyBf8H0egMHpHkNRlAyAHoA5xscRxzwiTrpxxBEaYghxtjgMoJyiqGKKohQArgGwJ+gxewB889T/fw3AO1y8JnhaI066ccQRGnsA/P/27dAGgQCGAuirYAIY5iSSKUjwKNQ5EmZAYNAkbMAOWIJhASQGRVLEhQ0uRwJ9E3xV8dvOo9Pg0WefC5n5whInXHHMzEtEbCLic8axxzgiblih7TNDGV4t0spfiogDppjgjjVGkJm76L40tpjhiUVmnr+TtvySGrqllDKgN65Ut8Pu8o2IAAAAAElFTkSuQmCC\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X_random[:,0], X_random[:,1], X_random[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### demean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def demean(X):\n",
    "    return X - np.mean(X, axis=0)\n",
    "\n",
    "X_demean = demean(X_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X_demean[:,0], X_demean[:,1], X_demean[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(w, X):\n",
    "    return np.sum((X.dot(w)**2)) / len(X)\n",
    "\n",
    "def df(w, X):\n",
    "    return X.T.dot(X.dot(w)) * 2. / len(X)\n",
    "\n",
    "def direction(w):\n",
    "    return w / np.linalg.norm(w)\n",
    "\n",
    "def first_component(X, initial_w, eta, n_iters = 1e4, epsilon=1e-8):\n",
    "    \n",
    "    w = direction(initial_w) \n",
    "    cur_iter = 0\n",
    "\n",
    "    while cur_iter < n_iters:\n",
    "        gradient = df(w, X)\n",
    "        last_w = w\n",
    "        w = w + eta * gradient\n",
    "        w = direction(w) \n",
    "        if(abs(f(w, X) - f(last_w, X)) < epsilon):\n",
    "            break\n",
    "            \n",
    "        cur_iter += 1\n",
    "\n",
    "    return w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 0.84785927,  0.33792667, -0.4085832 ])"
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "source": [
    "initial_w = np.random.random(X_demean.shape[1])\n",
    "eta = 0.01\n",
    "w1 = first_component(X_demean, initial_w, eta) \n",
    "w1 # 求出第一主成分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将原来的所有样本点X去除在第一主成分上的分量，得到X2\n",
    "X2 = np.empty(X_demean.shape)\n",
    "for i in range(len(X_demean)):\n",
    "    X2[i] = X_demean[i] - X_demean[i].dot(w1) * w1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 绘制X2，此时，X2的所有样本点分布在一个平面上\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X2[:,0], X2[:,1], X2[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 0.44401532, -0.03133187,  0.89547122])"
     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "source": [
    "w2 = first_component(X2, initial_w, eta)\n",
    "w2 # 求出第二主成分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将X2去除在第二主成分上的分量，得到X3\n",
    "X3 = np.empty(X2.shape)\n",
    "for i in range(len(X_demean)):\n",
    "    X3[i] = X2[i] - X2[i].dot(w2) * w2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 绘制X3，此时，X3的所有样本点分布在一条直线上\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X3[:,0], X3[:,1], X3[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.6.8 64-bit ('anaconda': conda)",
   "language": "python",
   "name": "python36864bitanacondaconda085db2e8b14649f4b32196068f7124e9"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}